MATHEMATICS

Jumat, 31 Oktober 2008

“Biarlah Newton ada! Dan semuanya akan terang benderang!”


ISAAC NEWTON
[1642-1727]


Isaac Newton merupakan ilmuwan paling besar dan paling berpengaruh yang pernah hidup di dunia. Ia lahir di Woolsthrope, Inggris, tepat pada hari Natal tahun 1642. Pada waktu masih bocah dia sudah menunjukkan kecerdasan dan kecakapannya di bidang mekanika dan sangat trampil dan cekatan menggunakan tangannya. Meskipun anak dengan otak yang cemerlang, di sekolah tampaknya ia ogah-ogahan dan tidak banyak menarik perhatian para gurunya. Sehingga ketika menginjak remaja, ibunya berniat mengeluarkannya dari sekolah dengan harapan anaknya bisa jadi petani yang baik. Untungnya sang ibu bisa dibujuk, kalau bakat utamanya tidak terletak di bidang pertanian-menggarap sawah.
Pada umur delapan belas tahun dia masuk Universitas Cambridge. Di sinilah Newton secara kilat menyerap ilmu pengetahuan dan matematika dan dengan cepat pula mulai melakukan penyelidikan sendiri. Antara usia dua puluh satu dan dua puluh tujuh tahun dia sudah meletakkan dasar-dasar teori ilmu pengetahuan yang pada gilirannya nanti akan mengubah dunia. Isaac Newton-lah orang yang sanggup menyuguhkan kumpulan teori yang terangkum rapi dan meletakkan batu pertama ilmu pengetahuan modern yang kini arusnya jadi anutan orang.
Newton sendiri sebenarnya agak ogah-ogahan menerbitkan dan mengumumkan penemuan-penemuannya. Gagasan dasar sudah disusunnya jauh sebelum tahun 1669, tetapi banyak teori-teorinya baru diketahui publik bertahun-tahun sesudahnya.

Kontribusi terbesar Newton di bidang matematika adalah penemuannya tentang "kalkulus integral" yang mungkin dipecahkannya ketika ia masih berumur dua puluh tiga atau dua puluh empat tahun. Penemuan ini merupakan hasil karya terpenting di bidang matematika modern. Bukan semata karena dari kalkulus integral itu tumbuh teori matematika modern, tetapi juga perangkat tak terelakkan yang tanpa penemuan itu mustahil pengetahuan modern berkembang dan mengalami kemajuan yang pesat. Selain itu, Newtonlah orang yang menemukan dalil binomial yang amat logis dan dapat dipertanggungjawabkan.
Tahun 1678 Newton menerbitkan buku karyanya yang sangat terkenal “Prinsip-prinsip matematika mengenai filsafat alamiah” (biasanya disingkat Principia). Dalam buku itu Newton mengemukakan teorinya tentang hukum gaya berat dan tentang hukum gerak. Dia menunjukkan bagaimana hukum-hukum itu dapat dipergunakan untuk memperkirakan secara tepat gerakan-gerakan planet-planet yang mengitari matahari.

Jika kita buka-buka indeks ensiklopedia ilmu pengetahuan, kita akan menjumpai hal menyangkut Newton beserta hukum-hukum dan penemuan-penemuannya dua atau tiga kali lebih banyak jumlahnya dibanding ilmuwan yang manapun juga. Banyak ilmuwan besar lain yang sejaman maupun yang hidup sesudahnya mengakui kehebatan Newton. Misalnya, Laplace, ilmuwan besar Perancis itu memuji, “Buku Principia Newton berada jauh di atas semua produk manusia genius yang ada di dunia." Langrange sering menyatakan bahwa Newton adalah genius terbesar yang pernah hidup. Tak ketinggalan Leibniz, salah seorang cendekiawan besar yang sama sekali tidak dekat, bahkan pernah terlibat dalam suatu pertengkaran sengit dengan Newton mengungkapkan, "Dari semua hal yang berkaitan dengan matematika, dari mulai dunia berkembang hingga adanya Newton, orang itulah yang memberikan sumbangan terbaik."
Newton bukan semata yang paling cerdas otak diantara barisan cerdas otak, tetapi sekaligus dia tokoh yang paling berpengaruh di dalam perkembangan teori ilmu pengetahuan. Newton menghembuskan nafas penghabisan tahun 1727, dikebumikan di Westminster Abbey, dialah ilmuwan pertama yang memperoleh penghormatan macam itu.


Selasa, 28 Oktober 2008

A programmer's view of the Universe, part 1: The fish

I write a column for computer programmers called "Stevey's Blog Rants." It's basically a magazine column — I publish to it about once a month. The average length of my articles is about 12 pages, although they can range anywhere from 4 to 40 pages, depending on how I'm feeling. But for precedent, don't think blogs: think of Reader's Digest. The blog format sets the wrong expectations.

Hence, some people complain that my articles are too long. Others complain that I have not given my arguments sufficient exposition, and that my articles are in fact too short on detail to warrant any credibility. This is a lose-lose situation for me, but I keep at it nonetheless because I enjoy writing. Even if nobody were to read my blog, the act of writing things down helps me think more clearly, and it's engaging in the same way that solving a Sudoku puzzle is engaging.

You should try it yourself. All it takes is a little practice.

My blog topics vary widely, and sometimes I even venture outside the realm of programming. Programming is where I'm most comfortable, and it's also where people seem to ascribe to me some level of punditry: I'm not necessarily right, but even my greatest detractors grudgingly admit that I'm entitled to an opinion, by virtue of my having spent twenty years hacking day and night without any sign of wanting to give it up and turn into a pointy-haired manager.

Even though I love both programming and to a lesser extent writing about it, there are also lots of non-programming topics I'd like to write about. Being a career programmer gives you an interesting perspective on issues not directly related to programming. You start to see parallels. So maybe I'll branch out some more and see how it goes.

The programmer's view

The first thing you notice as a programmer is that it trains you — forces you, really — to think in a disciplined way about complex logic problems. It also gives you a big booster shot of confidence around problem-solving in general. Junior programmers tend to have very high opinions of themselves; I was no exception.

In time, though, programming eventually humbles you, because it shows you the limits of your reasoning ability in ways that few other activities can match. Eventually every programmer becomes entangled in a system that is overwhelming in its complexity. As we grow in our abilities as programmers we learn to tackle increasingly complex systems. But every human programmer has limits, and some systems are just too hard to grapple with.

When this happens, we usually don't blame ourselves, nor think any less of ourselves. Instead we claim that it's someone else's fault, and it just needs a rewrite to help manage the complexity. In many cases this is even true.

Over time, our worldwide computer-programming community has discovered or invented better and better ways ways to organize programs and systems. We've managed to increase their functionality while keeping the complexity under control.

But even with such controls in place, systems can occasionally get out of hand. And sometimes they even need to be abandoned altogether, like a dog that's gone rabid. No matter how much time and love you've put into such systems, there's no fixing them.

Abandoning a system is a time of grieving for the folks who've worked on it. Such systems are like family.

And there's a disturbing lesson at the tail end of such experiences. The scary thing is that it's very easy, as a programmer standing at the precipice of complexity, to envision systems that are orders of magnitude more complex, millions of times more complex, even unimaginably more complex.

In the end, programming shows us how small we are.

The fish's view

Long ago, I used to have a Siamese fighting fish, also known as a Betta splendens, or simply a "betta". You can buy these fish at almost any pet store. I kept my betta, who was a deep vibrant red, in a pretty little 15-gallon tank decorated with a resplendence of real freshwater plants. And for a while I think my betta was happy there.

Like many Americans, I went through a phase in which I kept and ultimately killed many, many tropical fish. I didn't kill them intentionally; I wanted them to live and thrive. But keeping them alive for long is a challenge when you don't live in the tropics. So they might live for a few months or maybe a year, but they would always die prematurely. It was sad, and eventually I could no longer bear it, so I stopped keeping them.

Of all my fish, my betta left the biggest impression on me. The betta is a remarkable fish in several ways. For one thing, bettas are physically beautiful, and when they are at full display, their fins expand, peacock-like, into a fluid rose shape that is undeniably dramatic.

Bettas are also remarkable because they fight. They do not fight to establish a pecking order, as other fish do; they fight to kill. The males display their fins and then fight whenever they see another male betta, or even their own reflection, so they have to be kept alone and away from mirrors.

But bettas, I think, are most remarkable for their intelligence. Of all of the hundreds of tropical fish I kept, only bettas displayed anything resembling intellectual curiosity.

This really makes bettas some of the saddest stories in the tropical fish industry. Like other hobbyist fishes, they are stolen from their natural habitat and shipped overseas, or at best farmed in unsavory conditions. But unlike most other fish, bettas are also dyed to enhance their color. They are generally housed in tiny fist-sized bowls because of their ability to breathe air when necessary. And they are bred to express their fighting genes, and are often made to fight by their owners. Whereas other fish are kidnapped and sold, bettas are abused.

But worst of all, I believe their high intelligence endows them with greater capacity for suffering than other fish species. They can suffer physically and emotionally, but as we will see shortly, they can also suffer intellectually.

So bettas are a sad story.

My betta

Here is the specific sad story of my betta, the fish that left such an impression on me.

I had taken to lying on my bed and watching my betta for an hour or longer. The betta was the sole occupant of the tank in my bedroom. I had filled the tank with plants and copious natural light, so the effect was calming and serene. At times I almost envied the betta for the nice home I'd made for him.

One day, after the betta had been in his new home for several weeks, I found him exploring. It was a most unusual exploration, and one that I will never forget.

For the first few weeks, the betta explored the way you would expect any reasonably intelligent fish to go about the task. For the first few days he swam around to every nook and cranny of the tank, to make sure he had the lay of the land. Then for a few more days he experimented with staying put in different locations to see how he liked their feel.

Just like people, most fish will soon find a spot or a path they like best, and they'll stay in that spot or on that path for the rest of their lives.

But my betta was different. After his initial explorations he became restless. I'm no Fish Whisperer, but I could tell that he was restless. You would have thought so too. The betta started spending most of his time looking out of the tank, examining my bedroom. And he was clearly looking at specific things in the bedroom, not just "out there" in general. He would periodically swim around looking mildly agitated. He was acting like he wanted out.

I did everything I could to placate him. I experimented with different fish foods. I changed the water weekly and monitored it carefully to keep its temperature and pH within acceptable ranges. I added more lights. I added more plants. I rearranged the plants. In desperation, I even added a little castle.

Every time I tried something new, it would pique his interest for a little while. But in time, and faster each time than before, he would revert to his state of restlessness.

I'd never seen quite this behavior in other fish, so already he was demonstrating what seemed to be above average intelligence.

And then one day I found him engaged in an exploration that was altogether new.

He wasn't exploring the tank. He'd already investigated its topology for weeks. This time, he was exploring the nature of the tank. That's what caught my attention, and not just for that day, but for the rest of my life.

There was a twenty-inch vine in the tank that extended from the lower left back corner to the upper right front corner, along the diagonal of the main volume of the tank. The vine belonged to one of the many plants I'd put in there in the hopes of making it feel more like the Mekong river basin and less like a plexiglass tank in Seattle, Washington.

The betta had his nose on the vine. He was floating just above it, twitching his fins slightly to stay in place, and he was keeping his eyes as close to the vine as possible while keeping it in focus: about half a centimeter to a centimeter. And he was traversing the vine.

With the tiniest of motions, he was propelling himself along the vine towards the lower back right corner, keeping it under close scrutiny at all times. This excursion, from the halfway point to the end of the vine, took him perhaps three minutes. He was taking his time.

When he got to the end of the vine, he remained rooted in place while he inspected the 3-inch-radius spherical volume at the end of the vine, which was truncated in three dimensions by the walls and floor of the tank. He spent about three or four minutes doing this inspection, evidently making sure the vine really did terminate in the corner, and did not escape the tank.

After he had thoroughly scrutinized everything in the betta-sized vicinity of the vine's end, he turned back to the vine, nose pressed close, and began working his way along the vine in the other direction.

At this point I sat down to watch, because if he was doing what I thought he might be doing, then... I didn't know what to think. I wanted to see it for myself.

Over the next seven to ten minutes, he crept along the vine, never losing sight of it nor getting further than a centimeter from it, until he reached the upper-right front corner of the tank. He then proceeded to repeat his inspection of the volume at vine's end, ensuring himself that the vine terminated in the tank rather than protruding beyond the wall.

But what if he had missed something?

Sure enough, he turned and looked down the length of the vine for a time. And then he put his nose back on the vine and began again his long descent to the other end.

He did this for five days.

By the second day my amazement had turned to concern, and by the third day I felt utterly helpless. Here was an intelligent prisoner, my captive, exploring the mechanics of his prison with a thoroughness that only the imprisoned can afford, looking for an escape with deathly tenacity.

But while purchasing my betta had been easy enough, returning him to his real home would be unthinkably difficult, and probably unsuccessful even if I'd tried. Returning him to the fish store seemed like a dead end; he could easily wind up worse off than he was now.

So I concluded that there was nothing I could do. As he inspected the vine, I bit my nails, and timed passed in silence.

After the fifth day he gave up. And then he did something that I still don't understand, even though I've heard about this kind of thing before, and even though I personally saw him do it: he died of unhappiness.

It only took him a few days. He refused his food, he stopped moving, and to all external appearances he had become ill. But I knew better.

The lesson

Whenever I find myself struggling against the tide of massive system complexity, I think of my betta. He had a big heart, a small brain, and a small range of sensory input. I watched him use them all as methodically as any programmer to reason his way through to a soundness proof of the inescapability of his prison.

We like to think of ourselves as being pretty smart. Admit it. We do. But in the grand scheme of things we're intellectually little better off than that fish. We can easily find problems so complex that reasoning about them can take days or weeks of microscopic scrutiny, like my fish swimming along his vine.

And we can just as easily envision problems thousands or millions of times more complex: problems beyond the reasoning abilities of any person, any group of people, or even our entire species.

This has ramifications for the way we think about things today.

I believe I will have more to say about this soon. Right now I need to go mourn my fish, whose soul shone as brightly as that of anyone I've known.

Senin, 27 Oktober 2008

Soal Minggu Ini 28102008

Selisih dua bilangan positif adalah 5, sedangkan kuadratnya 2100 kurangnya dari kuadrat jumlah kedua bilangan itu. Berapakah jumlah kedua bilangan tersebut?

Selamat Mencoba!

Sabtu, 25 Oktober 2008

Ketika Dakon Menjadi Alat Peraga Matematika



Setiap kali digelar pelajaran Matematika, para siswa kelas IV, V, dan VI SD Negeri Tuyuhan, Desa Tuyuhan, Kecamatan Pancur, Kabupaten Rembang, Jawa Tengah, selalu siap di kelas. Bahkan mereka antusias.
Mereka tak lagi takut dengan pelajaran Matematika terutama dalam menentukan faktor persekutuan terbesar (FPB) dan soal kelipatan persekutuan terkecil (KPK). Bagian ini menuntut kemampuan seseorang membayangkan sesuatu.
Pembelajaran itu dibuat agar menyenangkan. ”Pokoknya, yang kalah harus menggendong yang menang loh, ya,” kata Miratus Solikah kepada Naimatul Badiah, Selasa (23/9).
Setelah suit, kedua siswi Kelas VI SD Negeri Tuyuhan itu segera memainkan alat permainan tradisional yang disebut dakon itu. Alat itu terbuat dari tripleks sepanjang sekitar 100 sentimeter dan lebar 25 sentimeter.
Di badan tripleks itu terdapat 75 lubang kecil yang terbagi menjadi tiga baris menjadi 25 lubang pada setiap baris. Di atas setiap lubang di barisan teratas dituliskan angka 1-25.
Adapun di bawah baris terakhir terdapat tiga lubang besar untuk wadah biji dakon yang biasanya dari biji pohon asem, sawo, dan batu kerikil atau kapur. Lubang-lubang itu terbuat dari bekas wadah agar-agar atau jeli, penganan anak-anak.
”Kami menyebut alat peraga itu sebagai dakon FPB dan KPK lantaran alat itu bisa digunakan untuk menghitung bilangan-bilangan itu tanpa membuat deret dan pohon faktor,” kata guru SD kelas V SD Negeri Tuyuhan Dwi Kartikasasi di Rembang.
Ia mengatakan, alat peraga itu dibuat Slamet, salah seorang pengajar di SD Tuyuhan. Alat itu bisa dibuat sesuai kebutuhan bilangan yang mau dihitung dengan cara menambah lubang, baik yang memanjang maupun yang membujur.
Cara memainkannya adalah dengan meletakkan biji-biji dakon satu per satu di lubang dakon sesuai dengan kelipatan atau perkalian faktor.

Syaratnya, siswa harus hafal kelipatan dan perkalian yang sudah diajarkan di kelas IV.
Misalnya, untuk menentukan KPK 2 dan 3, siswa harus meletakkan biji dakon sejumlah kelipatan 2 di lubang-lubang baris pertama sesuai nomor lubang dakon dan kelipatan dua, yaitu 2, 4, 6, 8, dan seterusnya.
Saat menjabarkan kelipatan 3, siswa menaruh biji dakon di lubang-lubang baris kedua sesuai nomor lubang dakon dan kelipatan 3, yaitu 3, 6, 9, 12, dan seterusnya.
”Dari baris lubang pertama dan kedua, siswa bisa menentukan KPK dengan melihat biji dakon yang letaknya satu kolom atau berada pada nomor lubang dakon yang sama,” kata dia.
Miratus Solikah dan Naimatul Badiah mengaku terbantu memahami pelajaran itu. Namun, alat itu masih terbatas lantaran tidak bisa untuk menghitung FPB dan KPK lebih dari 50.
”Kalaupun bisa, dakon harus dibuat panjang dengan 50 lubang. Tangan kami jadi tak sampai nanti,” kata Solikah sambil tersenyum. Apa pun kekurangannya, setidaknya Slamet telah membuat inovasi demi kemajuan anak didik.... (HENDRIYO WIDI)

Sumber: KOMPAS/ALBERTUS HENDRIYO WIDI
Selasa, 14 Oktober 2008 | 17:30 WIB

An interesting puzzle maker

Are you creating Jigsaw puzzles on your own???
Formulator Tarsia known earlier as Formulator Jigsaw is an editor designed for Teachers of Mathematics creating the activities in a form of jigsaws or dominos etc for later use in a class. It includes the powerful equation editor for building the math-expressions for the activities. An advanced feature of text placement along the side of the shape makes this tool irreplaceable software for fast activity creation. Formulator Tarsia became a powerful tool for learning activities since it supports the activity templates. It enables easy support of teachers and gives them new perspectives to development of their teaching activity.
This tool is very interesting!!!
To know more...Here is the link

Jumat, 24 Oktober 2008

Batik dan Matematika [Part 2]

BATIK WUJUD KOMPLEKSITAS SOSIAL
Oleh YUN HARIADI
Sering sebuah karya seni secara tidak sengaja menggunakan konsep matematika canggih yang baru dipahami beberapa abad kemudian. Seni dan matematika berkembang dengan berpijak pada pemikiran dengan segala keterbatasan dan kreativitasnya.

Konsep matematika harus logis, sementara seni tidak harus
demikian. Seni bisa berkembang demikian liar menembus batas logika
saat itu. Maka, tidak aneh jika matematika tertatih-tatih dan butuh
waktu cukup lama untuk memahami seni dalam konsep logikanya. Misalnya,
pada seni dekoratif Islam abad pertengahan yang ternyata menggunakan
geometri canggih (decagonal quasicrystal geometry) yang baru bisa
dipahami oleh matematikawan di era 70-an, pada jurnal ilmiah, atau
pada karya-karya Escher yang sampai saat ini susah untuk dipahami.
Bagaimana dengan batik? Adakah konsep matematika canggih pada
batik? Hasil penelitian yang dilakukan penulis dan rekan-rekan yang
diterbitkan dalam proceeding Generative X di Milan Italia (Pixel
People Project, "Batik Fractal: Traditional Art to Modern Complexity")
dan Journal of Social Complexity 2008 Bandung Fe Institute menunjukkan
kehadiran fraktal dalam batik.

Fraktal dan teori khaos
Istilah fraktal kali pertama dipopulerkan oleh Benoît Mandelbrot-
kemudian disebut sebagai Bapak Fraktal-pada pertengahan 70-an. Fraktal
merupakan konsep matematika yang membahas kesamaan pola pada semua
skala. Secara sederhana kehadiran fraktal ditandai dengan adanya
perulangan pola atau kesamaan diri (self-similarity) pada skala yang
berbeda-beda atas suatu obyek.
Contoh sederhana adalah segitiga Sierpinski. Pada segitiga ini,
setiap bagian segitiga di dalamnya memiliki kesamaan pola dengan
segitiga lainnya. Pohon cemara merupakan contoh sederhana hadirnya
fraktal di alam. Segitiga Sierpinski dan pohon cemara merupakan contoh
sempurna hadirnya fraktal. Kesamaan pola dan skala yang berbeda-beda
merupakan unsur penting dalam fraktal.

Perkembangan teknologi komputer telah memberikan sumbangan sangat
besar pada kelahiran fraktal. Perhitungan kesamaan pola pada skala
yang berbeda-beda makin tepat. Fraktal atau kesamaan pola pada skala
yang berbeda-beda menjadi begitu penting karena fraktal merupakan
tanda keteraturan dalam ketidakteraturan (khaos) dalam suatu sistem
yang bersifat khaos.
Suatu keadaan bersifat khaos jika sangat sensitif pada kondisi
awal. Pemeo yang begitu terkenal pada teori khaos misalnya "Kepakan
sayap kupu di Jakarta menyebabkan badai tornado di Texas".
Sebelum teori khaos ditemukan, kondisi khaos disamakan dengan
kondisi acak yang tanpa aturan, tanpa struktur, dan mustahil dibuat
model matematikanya. Namun setelah penemuan teori khaos kita paham
bahwa dalam sistem yang kompleks, tak-linier, dan sangat sensitif pada
kondisi awal ternyata terdapat tanda keteraturan dalam
ketidakteraturan, yaitu fraktal.

Dimensi fraktal
Geometri fraktal berbeda dengan geometri Euclidean yang kita kenal
selama ini. Geometri Euclidean hanya mampu mengelompokkan benda-benda
ke dalam dimensi bilangan bulat. Misalnya, kubus merupakan benda
berdimensi 3 (panjang-lebar-tinggi), gambar bujur sangkar berdimensi 2
(panjang-lebar), garis lurus berdimensi 1 (panjang). Geometri fraktal
menerima obyek berdimensi pecahan, misalnya 1,5 atau 2,75.
Menggunakan penggaris dimensi fraktal, maka tingkat fraktal suatu
benda bisa dibandingkan. Makin bernilai pecahan dimensi fraktal suatu
benda, maka makin tinggi pula tingkat fraktal benda tersebut.
Hasil perhitungan dimensi fraktal pada batik dengan sampel 200
motif menunjukkan bahwa batik memiliki dimensi fraktal 1,5. Sebagai
pembanding, yaitu lukisan kubisme Picasso, 1889-1930, yang memiliki
dimensi fraktal 3 (bilangan bulat). Hal ini menunjukkan batik memiliki
tingkat fraktal yang tinggi.
Sedangkan lukisan kubisme Picasso, sesuai kenyataan bahwa kubisme
adalah aliran lukisan yang menyederhanakan obyek ke dalam bentuk
silinder, kerucut, kubus, maupun bola-yaitu benda-benda berdimensi 3.
Dimensi permukaan lukisan kubisme dan batik pada semua sudut, dari 0°-
360° derajat.
Kubisme taat dengan dimensi 3, sedangkan batik taat dengan dimensi
1,5. Ini menunjukkan motif batik tidak cukup digambarkan oleh benda
berdimensi 1, namun berlebihan jika digambarkan oleh benda berdimensi
2.
Faktor yang berperan besar menghadirkan fraktal pada batik adalah
teknik dekorasi yang berhubungan dengan makna simbolis pada batik,
yaitu isen, yaitu mengisi motif besar dengan motif kecil tertentu. Ini
sesuai-mirip dengan kesamaan-diri pada fraktal meski tidak sesempurna
segitiga Sierpinski.
Proses isen, menurut Haldani, ahli batik tradisional dari Institut
Teknologi Bandung, merupakan upaya penyempurnaan dan memberi makna
obyek keseluruhan. Isen dalam batik motif semu riris merupakan motif
kecil dalam motif besar.

Kompleksitas sosial
Batik muncul sebagai hasil interaksi antarmanusia
denganlingkungannya. Manusia memahami alam lingkungan dan
menerjemahkannya dengan melukis dengan teknik batik. Obyek batik
merupakan benda-benda di alam-berdimensi 3 (pohon, hewan) yang
sebagian besar memiliki makna simbolis tertentu.
Dinamika masyarakat dan lingkungannya jelas berpengaruh pada
batik. Kebudayaan- kebudayaan besar (Hindu, Islam, kolonial Belanda,
Jepang, Kemerdekaan, Orba) berpengaruh pada corak, warna, dan motif
pada batik, namun batik mampu mempertahankan dimensi fraktalnya pada
sekitar 1,5. Ini menunjukkan adanya aturan da- sar dalam batik sendiri
yang sedemikian sehingga dimensi fraktal batik tetap pada nilai
sekitar 1,5.

Interaksi antara manusia dan lingkungan dalam menghasilkan batik
merupakan interaksi tak-linier, melibatkan banyak faktor yang saling
berkaitan, seperti teknologi (canting, lilin, pewarna), budaya
(simbolisme), kepercayaan (mistisme), ekonomi, dan geografi.
Kehadiran fraktal dalam batik merupakan wujud adanya kompleksitas
sosial dalam batik sehingga untuk memahami batik harus melihat faktor
teknologi, budaya, kepercayaan, ekonomi, geografi secara bersama-sama.
Kompleksitas sosial lainnya yang ditandai oleh kehadiran fraktal
misalnya evolusi sebuah kota. Hasil penelitian Profesor Michael Batty,
diterbitkan dalam jurnal Science, menunjukkan, kota merupakan sistem
kompleks yang melibatkan faktor ekonomi, sosial, hingga perubahan
iklim. Faktor-faktor tersebut berpengaruh pada ukuran, skala, dan
bentuk sebuah kota sehingga juga membutuhkan geometri fraktal.

YUN HARIADI
Peneliti Kompleksitas Sosial Pixel People Project

***
Isen dalam batik motif semu riris merupakan motif kecil dalam motif
besar. Hal ini mirip dengan kesamaan-diri pada fraktal. Kesamaan-diri
ini meskipun jauh sempurna dibandingkan dengan segitiga Sierpinski dan
pohon cemara, namun berkontribusi pada pembentukan pola fraktal.
Kesamaan-diri tidak harus diukur berdasarkan kesamaan secara visual,
namun bisa diukur pada sifat-sifat statistikanya.

***
Segitiga Sierpinski dan pohon cemara merupakan contoh sempurna
hadirnya fraktal.

Kompas, 10 Maret 2008

Kamis, 23 Oktober 2008

Batik dan Matematika [Part 1]

Batik ternyata tidak melulu berkaitan dengan seni tradisional. Selama ini kita hanya mengenal batik tulis dan batik cap dengan proses pengerjaan murni buatan tangan.
Namun ternyata, dengan hitungan matematika motif batik dapat dibuat dengan mudah lewat komputer. Hasilnya, motif batik dapat dibuat dengan waktu relatif cepat, dan mudah diperbanyak. Tak hanya itu, selain bisa diaplikasikan di selembar kain, motif batik buatan komputer ini juga bisa diaplikasikan di media kayu dan akrilik.
Tiga serangkai asal Bandung , Muhammad Lukman, Nancy Margried Panjaitan, dan Yun Hariadi mencoba "memodernkan" batik. Setelah melalui penelitian yang panjang sejak tahun 2007, mereka pun meluncurkan batik fraktal, suatu batik dengan desain geometri yang terus berulang, pada Mei silam di Bandung.

Menurut Head of Business Pixel People Project Research & Design Nancy Margried Panjaitan, semula mereka bertiga hanya teman ngobrol di sela-sela acara desain dan mode yang banyak digelar di Bandung. Akhirnya mereka bertiga membentuk kelompok kerja yang bernama Pixel People Project tahun 2007 lalu. Selain batik fraktal, mereka menghasilkan karya, seperti robot, desain gedung dan sebagainya. "Kami tak memiliki satu pemimpin dan tak memiliki kantor," tutur Nancy.

Mereka menganut konsep mobile office. Untuk mengerjakan sesuatu, mereka cukup mengkoordinasikan pekerjaan lewat alat komunikasi dan bertemu muka sesekali saja.
Ketika mendirikan usaha, mereka bertiga harus banyak bertaruh. Nancy dan Luki rela meninggalkan pekerjaan lamanya sebagai karyawan dan berpindah menjadi pengusaha. Modal awal senilai Rp 20 juta berasal dari membobol tabungan masing-masing, sebagian besar dihabiskan untuk penelitian. Tak sampai satu tahun perusahaan bisa menutup modal usaha. Maklum, mereka membanderol produknya dengan harga tinggi, yakni antara Rp 500.000 dan Rp 20 juta per lembar kain batik.


Di tengah penelitian mereka tentang motif batik, mereka bertiga sempat diundang untuk mempresentasikan penemuannya dalam 10th Generative Art Conference, Politecnico, di Milan, Italia, Desember 2007 lalu.


Semenjak batik fraktal diluncurkan mereka mendapat dukungan dari Kementerian Riset dan Teknologi. Tiga serangkai ini kemudian ditawari untuk melakukan pameran, Mei 2008. Semua kegiatan selama pameran berlangsung disponsori oleh Kementerian Riset dan Teknologi

Karena usia batik fraktal yang baru tiga bulan, Nancy mengatakan usaha ini masih dalam situasi yang menantang. Mereka kesulitan mencari investor untuk menanam modalnya dalam pemasaran dan pengembangan produk ini. Sejak tahun lalu, mereka telah mengajukan sejumlah proposal pendanaan tambahan ke sejumlah perusahaan.

Namun, konsep ini belum diapresiasi dengan baik oleh para pemodal. Alasan mereka, tutur Nancy, inovasi ini belum teruji sehingga terlalu beresiko untuk dibantu secara permodalan. "Menurut saya itulah resiko sebuah inovasi baru. Tapi kami terus mengembangkan karya kami dan terus mencari investor yang sesuai untuk usaha ini," kata Nancy.

Menristek pemakai batik fraktal pertama
Untuk memasarkan usaha batik fraktalnya, mereka melakukan bermacam jurus. Selain lewat pameran, penjualan juga dilakukan secara personal, made to order, pemesanan khusus, pemasaran lewat internet, dan bekerja sama dengan beberapa desainer dan butik fesyen yang ada di Jakarta. "Hingga saat ini, pembeli kain batik fraktal kebanyakan pemakai perorangan," tutur Nancy.

Bahkan, hingga kini Menteri Ristek Kusmayanto Kadiman merupakan salah satu pelanggan setia batik fraktal ini. Ungkap Nancy, "Menristek adalah orang pertama yang memakai kemeja batik fraktal di hadapan publik lho."
Kini, selain membatik di atas kain, mereka juga membatik di atas media kayu dan akrilik. Bedanya, jika biasanya mereka menggunakan canting untuk menggambar motif batik fraktal di atas kain, maka untuk media kayu dan akrilik ini mereka menggunakan laser.
"Rencananya, batik fraktal akan dikembangkan dalam industri interior, furnitur, sepatu dan berbagai industri lainnya," kata Nancy.

Sumber: Kompas, Rabu, 10 September 2008 | 09:06 WIB

Rabu, 22 Oktober 2008

Matematika Di Sekolah Terbatas

Matematika di Sekolah Terbatas
Keberadaan Kursus Sangat Membantu Siswa


Pembelajaran Matematika di sekolah sangat terbatas sehingga kebutuhan anak terhadap Matematika belum seluruhnya terpenuhi. Keberadaan kursus-kursus Matematika seperti Kumon, Sakamoto, Jarimatika, dan yang lainnya menjadi sarana yang membantu anak belajar.

Seperti diwartakan sebelumnya, semakin banyak berdiri lembaga kursus yang sebagian merupakan waralaba dari negara lain. Lembaga kursus tersebut menawarkan berbagai metode pembelajaran Matematika alternatif, seperti Sakamoto, Kumon, Jarimatika, dan lain-lain.

Ketua Asosiasi Guru Matematika Indonesia, Firman, mengatakan, pola pembelajaran Matematika di sekolah diakui masih kurang menyenangkan bagi anak. Hal itu dikarenakan pembelajaran Matematika di sekolah seolah- olah direduksi hanya persoalan hitung-menghitung.

”Banyak anak yang mengartikan belajar Matematika itu menghafal rumus dan menghitungnya, kemudian selesai. Aktivitas yang bersifat mekanistik tersebut membosankan anak. Padahal, belajar Matematika ialah bagaimana anak dengan informasi yang dia bangun mampu menyelesaikan permasalahan,” ujarnya.

Prinsipnya adalah pembangunan pola pikir anak dalam memecahkan masalah.

Hanya saja, dengan adanya sistem evaluasi yang dibangun pemerintah sekarang, mulai dari ulangan umun, ujian nasional (UN), dan seleksi masuk perguruan tinggi negeri semuanya kemudian mengarah ke pola mekanistis. Guru juga sibuk mempersiapkan murid agar siap menghadapi berbagai ujian tersebut dengan drilling berlatih menjawab soal dengan benar dan cepat.


Abdul Hakim Gani, guru Matematika SMAN 17 Jakarta dan pengajar di sejumlah sekolah swasta, mengatakan hal senada.

Belajar kreatif

Kurikulum Tingkat Satuan Pendidikan (KTSP) sebetulnya memberikan kesempatan kepada pembelajaran kreatif. ”Kesulitannya ialah adanya tuntutan berbagai ujian, sehingga larinya malah ke arah keterampilan. Tuntutan kurikulum malah sulit dipenuhi,” ujarnya.

KTSP yang disusun oleh guru sendiri sebetulnya menawarkan konsep agar anak berkembang menurut tingkat kemampuannya sendiri sehingga dimungkinkan percepatan atau remedial. Terutama remedial yang sangat penting dalam pembelajaran Matematika.

Dia berpendapat, jika anak belajar pada level pengetahuannya, anak tidak akan terlalu takut terhadap Matematika. ”Kalau anak belajar tidak sesuai dengan levelnya, anak ketakutan dan terjadi penumpukan materi yang tidak dikuasai,” katanya.

Sumarsono, guru SMPN 89 Jakarta Barat, berpendapat, belajar Matematika seharusnya diawali dengan pemberian motivasi. Guru, terutama, harus dapat menggambarkan kepada anak didiknya manfaat belajar Matematika dalam kehidupan.

”Saya selalu menekankan kepada para murid, sadar atau tidak, mereka membutuhkan pelajaran tersebut,” ujarnya. Belajar Matematika juga dimulai dengan hal yang mudah dan beranjak ke materi lebih sulit.

Keberadaan kursus

Firman berpendapat, masih perlu diteliti lagi apakah keikutsertaan anak di lembaga kursus yang menyajikan metode Matematika alternatif tersebut berpengaruh kepada prestasi di bidang Matematika.

”Tetapi, berdasarkan pengalaman saya mengajar selama ini di sekolah menengah atas, biasanya anak yang kursus mempunyai keterampilan berhitung sangat baik. Mereka lebih mudah melihat pola-pola dalam belajar Matematika,” ujarnya.

Kelebihan lain dari kemampuan menghitung cepat itu adalah anak cenderung bermotivasi dan bersemangat belajar Matematika. ”Itu karena mereka mampu menyelesaikan soal sulit dalam waktu cepat sehingga muncul rasa percaya diri,” ujarnya.

Hal senada diungkapkan Abdul Gani. ”Biasanya, terlihat perbedaan pada kemampuan awalnya atau entry behavior. Anak yang kursus Matematika sangat menguasai materi aritmatika,” ujar Abdul Gani.

Sumarsono berpendapat, metode belajar Matematika berbeda di sekolah pada umumnya dan di tempat kursus. Di tempat kursus, rasio tutor dan peserta lebih sedikit.

”Relasi serta komunikasi antara tutor dan peserta kursus lebih informal. Lingkungan dan metode belajar juga lebih bervariasi,” ujarnya. (INE)

Sumber: Kompas, Kamis, 23 Oktober 2008 | 01:04 WIB

De Britto EduFair 2008: A Gateway to Bright Future

Salah satu tujuan pendidikan di Sekolah Menengah Atas (SMA) adalah menghantarkan siswa agar mampu melanjutkan pendidikannya ke Perguruan Tinggi (PT). Untuk itu, memberi bekal pengetahuan, informasi, kemandirian, dan nilai-nilai hidup adalah pilihan yang tidak dapat ditawar-tawar.

Terdorong oleh keinginan untuk memberikan informasi yang utuh dan mendalam, sekaligus untuk memberi kesempatan PT-PT atau lembaga-lembaga perwakilan asing yang belum berkesempatan memberikan presentasi, maka kegiatan ini dibuat.

Informasi yang jelas, jujur, dan terbuka lembaga pendidikan tinggi, baik negeri maupun swasta; dalam maupun luar negeri serta perwakilan lembaga pendidikan asing akan sangat membantu para siswa dalam menentukan pilihan yang tepat. Informasi ini tentu juga akan bermanfaat bagi siswa-siswa yang masih duduk di kelas X maupun XI karena mereka pun akan menentukan pilihan untuk studi lanjut di kemudian hari. Pun orang tua sebagai pendidik yang utama tentu akan memperoleh informasi yang akurat dalam mendukung pengembangan bakat dan minat putra-putranya.


Yogyakarta adalah kota pelajar. Kegiatan ini juga akan diinformasikan ke SMA/SMK lain yang sangat banyak di kota ini. Sehingga di sisi lain, kegiatan ini juga akan menjadi sarana yang baik untuk mengenalkan lembaga-lembaga pendidikan tinggi dan pihak-pihak lain yang ingin mendukung dan terlibat/berpartisipasi dalam kegiatan ini.

Bentuk Kegiatan

Untuk mendukung pemikiran di atas digagas kegiatan dalam bentuk pameran pendidikan yang selanjutnya disebut dengan ”De Britto Education Fair 2008”. Kegiatan ini secara spesifik diwujudkan dalam:

1. Informasi Jurusan Perguruan Tinggi dan Peluang Kerjanya
2. Pameran Pendidikan Tinggi

Untuk mendukung kegiatan ini, dalam waktu yang sama akan diselenggarakan:

1. Bazar Buku
2. Bazar makanan/minuman
3. Pentas Musik
4. Pameran Majalah Dinding.

Lingkup Kegiatan

Lingkup kegiatan ini dapat dipaparkan sebagai berikut:

1. Informasi tentang jurusan dan strategi belajar di PT berikut peluang kerjanya akan disampaikan oleh nara sumber-nara sumber yang ditunjuk dan dipilih, sharing alumni De Britto yang masih kuliah sesuai dengan jurusannya dan hanya diperuntukkan siswa kelas XII SMA Kolese De Britto secara intern.

2. Informasi dalam Education Fair ditekankan pada bidang studi yang ditawarkan, spesialisasi dan kekhasannya, persyaratan pendaftaran, lama dan biaya studi, juga status akreditasinya. Bentuk Education Fair dapat dilakukan dengan pemberian brosur/prospektus, konsultasi pendidikan, demonstrasi/peragaan alat, dan presentasi dengan jadwal yang sudah disusun.

3. PT/lembaga perwakilan PT asing yang direncakan terlibat dalam kegiatan ini adalah PT negeri/swasta di Yogyakarta, Solo, Semarang, Salatiga, Surabaya, Jakarta – Bogor – Depok – Tangerang - Bekasi (Jabodetabek), dan Bandung (kurang lebih 40 PT/perwakilan PT asing)

4. Education Fair terbuka untuk umum dan akan diinformasikan ke berbagai SMA/SMK se DIY, dan disebarluaskan lewat pamlet, spanduk, media massa baik koran, radio, maupun televisi

5. Bazar buku diperuntukkan bagi lembaga penerbitan yang memiliki referensi tentang strategi belajar di PT dan pendidikan secara umum

6. Bazar makanan/minuman terbuka untuk umum. Diperuntukkan bagi semua pengunjung dan peserta Education Fair, dalam rangka mememenuhi kenyamanan dalam mengunjungi stand-stand pameran

7. Pentas Musik dengan menampilkan band seleksi siswa SMA De Britto, beberapa band SMA di Yogyakarta, dan direncanakan pula mengundang Band ternama, dalam rangka menjaring pengunjung sebanyak-banyaknya.

8. Pameran Majalah Dinding diperuntukkan bagi semua kelas SMA De Britto. Selain untuk mengembangkan bakat siswa, pameran ini juga dimaksudkan untuk menarik pengunjung di luar De Britto.

9. Bazar Tanaman Hias terbuka untuk umum dan bertujuan menarik pengunjung, khususnya kalangan orangtua siswa.

Waktu dan Tempat Penyelenggaraan

1. Informasi jurusan dan peluang kerja
Hari/tanggal : Kamis, 23 Oktober 2008 (intern)
Sabtu, 25-Minggu, 26 Oktober 2008 (umum)
Tempat : Aula SMA Kolese De Britto
Waktu : Pukul 09.00 WIB - selesai.
Bentuk : Ceramah & Sharing
Pemateri : Nara sumber yang ditunjuk
Alumni dari berbagai PT dan disiplin ilmu.
Lingkup : Siswa kelas XII (intern) dan umum

2. Education Fair
Hari/tanggal : Sabtu, 25 s/d Minggu, 26 Oktober 2008
Waktu : Sabtu, Pukul 09.00 – 20.00 WIB
Minggu, Pukul 08.30-17.00 WIB
Tempat : Ruang kelas dan aula SMA De Britto
Peserta : PTN/PTS/Perwakilan lembaga pendidikan asing
(kurang lebih 50 PT)
Lingkup : terbuka untuk umum (SMA/SMK + 50 sekolah)

Selama Education Fair akan diselenggakan presentasi PT dengan tempat dan jadwal yang telah ditentukan.

3. Bazar Buku
Diadakan selama Education Fair dan bertempat di Aula, dengan target peserta kurang lebih 10 penerbit.

4. Bazar Makanan/Minuman
Diadakan selama Education Fair, bertempat di kantin dan halaman sekolah.

5. Pentas Musik
Hari/tanggal : Sabtu, 25 Oktober 2008
Tempat : Panggung Terbuka SMA De Britto
Peserta : Band Siswa SMA De Britto, beberapa Band SMA di Yogyakarta, Band bintang tamu
Lingkup : terbuka untuk umum

6. Pameran Majalah Dinding
Diadakan selama Education Fair, bertempat di depan kelas X, XI IPS dan Bahasa. Peserta adalah siswa SMA De Britto sebanyak 46 mading.

7. Bazar Tanaman Hias
Diadakan selama Education Fair, bertempat di tepi lapangan sepak bola, sebanyak 10 stand, dan diperuntukkan untuk umum.

Jadwal Presentasi

a. Di ruang Rapat

Sesi Hari/Tanggal Waktu
Sabtu, 25 Oktober 2008
1. 11.00 - 12.00
2 12.15 - 13.15
3 13.30 - 14.30
4 14.45 - 15.45
5 16.00 - 17.00
Minggu, 26 Oktober 2008
6 09.30 - 10.30
7 10.45 -11.45
8 12.00 - 13.00
9 13.15 - 14.15
10 14.30 - 15.30


b. Di ruang Perpustakaan

Sesi Hari/Tanggal Waktu
Sabtu, 25 Oktober 2008
1 10.30 - 11.30
2 11.45 - 12.45
3 13.00 - 14.00
4 14.15 - 15.15
5 15.30 - 16.30
Minggu, 26 Oktober 2008
6 10.00 - 11.00
7 11.15 -12.15
8 12.30 - 13.30
9 13.45 - 14.45
10 15.00 - 16.00


Akhirnya, siswa adalah subjek pendidikan. Demikian juga kegiatan ini direncanakan dan diselenggarakan semata-mata untuk siswa. Dengan kegiatan ini diharapkan siswa-siswi di SMA/SMK di Daerah Istimewa Yogyakarta (DIY) pada umumnya, dan siswa-siswa SMA Kolese De Britto pada khususnya memperoleh bekal pengalaman, informasi yang lengkap, jujur, dan terbuka untuk menentukan pilihan kelanjutan pendidikannya.

Bulan Oktober sampai Januari adalah bulan-bulan yang sungguh tepat untuk membekali siswa dengan informasi tentang pendidikan tinggi. Semakin banyak informasi yang didapatkan tentu akan memperluas kesempatan siswa untuk memilih. Semoga tema yang dipilih sungguh menjadi ispirasi bagi siswa untuk mulai memikirkan kelanjutan pendidikannya. “ A Gateway to Bright Future”.

Lingkup kegiatan ini cukup besar, dengan target 10.000 pengunjung. Untuk itu, kesempatan ini juga bisa dioptimalkan oleh berbagai pihak untuk mendukung kegiatan ini. Dukungan dari banyak pihak tentulah akan membawa kegiatan ini sampai pada tujuan yang diharapkan. Semoga!

PANITIA
DE BRITTO Education Fair 2008
Sekretariat: SMA Kolese De Britto, Jl. Laksda Adisucipto 161 Yogyakarta 55281
Telp. (0274) 518667 Fax. (0274) 547606 Web: www.debritto.yog_sch.net

Ujian Nasional 2009

Setelah sempat terdengar " kabar burung " bahwa jadwal Ujian Nasional akan dimajukan waktu pelaksanaannya, Departemen Pendidikan Nasional akhirnya mengumumkan waktu pelaksanaan " Hari penentuan " tersebut. Berikut isi petikan pengumuman dari Depdiknas :

Senin, 20 Oktober 2008

Misteri Bilangan Nol

Misteri Bilangan Nol
Oleh: Yusmichad Yusdja
Staf peneliti pada Pusat Penelitian dan Pengembangan Sosial dan ekonomi Pertanian IPB

Ratusan tahun yang lalu, manusia hanya mengenal 9 lambang bilangan yakni 1, 2, 2, 3, 5, 6, 7, 8, dan 9. Kemudian, datang angka 0, sehingga jumlah lambang bilangan menjadi 10 buah. Tidak diketahui siapa pencipta bilangan 0, bukti sejarah hanya memperlihatkan bahwa bilangan 0 ditemukan pertama kali dalam zaman Mesir kuno. Waktu itu bilangan nol hanya sebagai lambang. Dalam zaman modern, angka nol digunakan tidak saja sebagai lambang, tetapi juga sebagai bilangan yang turut serta dalam operasi matematika. Kini, penggunaan bilangan nol telah menyusup jauh ke dalam sendi kehidupan manusia. Sistem berhitung tidak mungkin lagi mengabaikan kehadiran bilangan nol, sekalipun bilangan nol itu membuat kekacauan logika. Mari kita lihat.

Nol, penyebab komputer macet
Pelajaran tentang bilangan nol, dari sejak zaman dahulu sampai sekarang selalu menimbulkan kebingungan bagi para pelajar dan mahasiswa, bahkan masyarakat pengguna. Mengapa? Bukankah bilangan nol itu mewakili sesuatu yang tidak ada dan yang tidak ada itu ada, yakni nol. Siapa yang tidak bingung? Tiap kali bilangan nol muncul dalam pelajaran Matematika selalu ada ide yang aneh. Seperti ide jika sesuatu yang ada dikalikan dengan 0 maka menjadi tidak ada. Mungkinkah 5*0 menjadi tidak ada? (* adalah perkalian). Ide ini membuat orang frustrasi. Apakah nol ahli sulap?
Lebih parah lagi-tentu menambah bingung-mengapa 5+0=5 dan 5*0=5 juga? Memang demikian aturannya, karena nol dalam perkalian merupakan bilangan identitas yang sama dengan 1. Jadi 5*0=5*1. Tetapi, benar juga bahwa 5*0=0. Waw. Bagaimana dengan 5o=1, tetapi 50o=1 juga? Ya, sudahlah. Aturan lain tentang nol yang juga misterius adalah bahwa suatu bilangan jika dibagi nol tidak didefinisikan. Maksudnya, bilangan berapa pun yang tidak bisa dibagi dengan nol. Komputer yang canggih bagaimana pun akan mati mendadak jika tiba-tiba bertemu dengan pembagi angka nol. Komputer memang diperintahkan berhenti berpikir jika bertemu sang divisor nol.

Bilangan nol: tunawisma
Bilangan disusun berdasarkan hierarki menurut satu garis lurus. Pada titik awal adalah bilangan nol, kemudian bilangan 1, 2, dan seterusnya. Bilangan yang lebih besar di sebelah kanan dan bilangan yang lebih kecil di sebelah kiri. Semakin jauh ke kanan akan semakin besar bilangan itu. Berdasarkan derajat hierarki (dan birokrasi bilangan), seseorang jika berjalan dari titik 0 terus-menerus menuju angka yang lebih besar ke kanan akan sampai pada bilangan yang tidak terhingga. Tetapi, mungkin juga orang itu sampai pada titik 0 kembali. Bukankah dunia ini bulat? Mungkinkah? Bukankah Columbus mengatakan bahwa kalau ia berlayar terus-menerus ia akan sampai kembali ke Eropa?
Lain lagi. Jika seseorang berangkat dari nol, ia tidak mungkin sampai ke bilangan 4 tanpa melewati terlebih dahulu bilangan 1, 2, dan 3. Tetapi, yang lebih aneh adalah pertanyaan mungkinkan seseorang bisa berangkat dari titik nol? Jelas tidak bisa, karena bukankah titik nol sesuatu titik yang tidak ada? Aneh dan sulit dipercaya? Mari kita lihat lebih jauh.


Jika di antara dua bilangan atau antara dua buah titik terdapat sebuah ruas. Setiap bilangan mempunyai sebuah ruas. Jika ruas ini dipotong-potong kemudian titik lingkaran hitam dipindahkan ke tengah-tengah ruas, ternyata bilangan 0 tidak mempunyai ruas. Jadi, bilangan nol berada di awang-awang. Bilangan nol tidak mempunyai tempat tinggal alias tunawisma. Itulah sebabnya, mengapa bilangan nol harus menempel pada bilangan lain, misalnya, pada angka 1 membentuk bilangan 10, 100, 109, 10.403 dan sebagainya. Jadi, seseorang tidak pernah bisa berangkat dari angka nol menuju angka 4. Kita harus berangkat dari angka 1.

Mudah, tetapi salah
Guru meminta Ani menggambarkan sebuah garis geometrik dari persamaan 3x+7y = 25. Ani berpikir bahwa untuk mendapatkan garis itu diperlukan dua buah titik dari ujung ke ujung. Tetapi, setelah berhitung-hitung, ternyata cuma ada satu titik yang dilewati garis itu, yakni titik A(6, 1), untuk x=6 dan y=1. Sehingga Ani tidak bisa membuat garis itu. Sang guru mengingatkan supaya menggunakan bilangan nol. Ya, itulah jalan keluarnya. Pertama, berikan y=0 diperoleh x=(25-0)/3=8 (dibulatkan), merupakan titik pertama, B(8,0). Selanjutnya berikan x=0 diperoleh y=(25-3.0)/7=4 (dibulatkan), merupakan titik kedua C(0,4). Garis BC, adalah garis yang dicari. Namun, betapa kecewanya sang guru, karena garis itu tidak melalui titik A. Jadi, garis BC itu salah.
Ani membela diri bahwa kesalahan itu sangat kecil dan bisa diabaikan. Guru menyatakan bahwa bukan kecil besarnya kesalahan, tetapi manakah yang benar? Bukankah garis BC itu dapat dibuat melalui titik A? Kata guru, gunakan bilangan nol dengan cara yang benar. Bagaimana kita harus membantu Ani membuat garis yang benar itu? Mudah, kata konsultan Matematika. Mula-mula nilai 25 dalam 3x+7y harus diganti dengan hasil perkalian 3 dan 7 sehingga diperoleh 3x+7y=21.
Selanjutnya, dalam persamaan yang baru, berikan y=0 diperoleh x=21/3=7 (tanpa pembulatan) itulah titik pertama P(6,1). Kemudian berikan nilai x=0 diperoleh y=21/7 = 3 (tanpa pembulatan), itulah titik kedua Q(0, 3). Garis PQ adalah garis yang sejajar dengan garis yang dicari, yakni 3x+7y=25. Melalui titik A tarik garis sejajar dengan PQ diperoleh garis P1Q1. Nah, begitulah. Sang murid telah menemukan garis yang benar berkat bantuan bilangan nol.
Akan tetapi, sang guru masih sangat kecewa karena sebenarnya tidak ada satu garis pun yang benar. Bukankah dalam persamaan 3x1+7x2=25 hanya ada satu titik penyelesaian yakni titik A, yang berarti persamaan 3x1+7x2 itu hanya berbentuk sebuah titik? Bahkan pada persamaan 3x1+7x2=21 tidak ada sebuah titik pun yang berada dalam garis PQ. Oleh karena itu, garis PQ dalam sistem bilangan bulat, sebenarnya tidak ada. Aneh, bilangan nol telah menipu kita. Begitulah kenyataannya, sebuah persamaan tidak selalu berbentuk sebuah garis.

Bergerak, tetapi diam
Bilangan tidak hanya terdiri atas bilangan bulat, tetapi juga ada bilangan desimal antara lain dari 0,1; 0,01; 0,001; dan seterusnya sekuat-kuat kita bisa menyebutnya sampai sedemikian kecilnya. Karena sangat kecil tidak bisa lagi disebut atau tidak terhingga dan pada akhirnya dianggap nol saja. Tetapi, ide ini ternyata sempat membingungkan karena jika bilangan tidak terhingga kecilnya dianggap nol maka berarti nol adalah bilangan terkecil? Padahal, nol mewakili sesuatu yang tidak ada? Waw. Begitulah.
Berdasarkan konsep bilangan desimal dan kontinu, maka garis bilangan yang kita pakai ternyata tidak sesederhana itu karena antara dua bilangan selalu ada bilangan ke tiga. Jika seseorang melompat dari bilangan 1 ke bilangan 2, tetapi dengan syarat harus melompati terlebih dahulu ke bilangan desimal yang terdekat, bisakah? Berapakah bilangan desimal terdekat sebelum sampai ke bilangan 2? Bisa saja angka 1/2. Tetapi, anda tidak boleh melompati ke angka 1/2 karena masih ada bilangan yang lebih kecil, yakni 1/4. Seterusnya selalu ada bilangan yang lebih dekat... yakni 0,1 lalu ada 0,01, 0,001, ..., 0,000001. demikian seterusnya, sehingga pada akhirnya bilangan yang paling dekat dengan angka 1 adalah bilangan yang demikian kecilnya sehingga dianggap saja nol. Karena bilangan terdekat adalah nol alias tidak ada, maka Anda tidak pernah bisa melompat ke bilangan 2?
Disadur dari: http://www.duniaesai.com/sains/sains16.htm

The Universal Design Pattern



  This idea that there is generality in the specific is of far-reaching importance.
Douglas Hofstadter, Gödel, Escher, Bach


Note: Today's entry is a technical article: it isn't funny. At least not intentionally.

Update, Oct 20th 2008: I've added an Updates section, where I'll try to track significant responses, at least for a week or so. There are three entries so far.

Contents



Introduction


Today I thought I'd talk about a neat design pattern that doesn't seem to get much love: the Properties Pattern. In its fullest form it's also sometimes called the Prototype Pattern.

People use this pattern all over the place, and I'll give you a nice set of real-life examples in a little bit. It's a design pattern that's useful in every programming language, and as we'll see shortly, it's also pretty darn useful as a general-purpose persistence strategy.

But even though this pattern is near-universal, people don't talk about it very often. I think this is because while it's remarkably flexible and adaptable, the Properties Pattern has a reputation for not being "real" design or "real" modeling. In fact it's often viewed as a something of a shameful cheat, particularly by overly-zealous proponents of object-oriented design (in language domains) or relational design (in database domains.) These well-meaning folks tend to write off the Properties Pattern as "just name/value pairs" – a quick hack that will just get you into trouble down the road.

I hope to offer a different and richer perspective here. With luck, this article might even help begin the process making the Properties Pattern somewhat fashionable again. Time will tell.

Three Great Schools of Software Modeling


Before I tell you anything else about the Properties Pattern, let's review some of the most popular techniques we programmers have for modeling problems.

I should point out that none of these techniques is tied to "static typing" or "dynamic typing" per se. Each of these modeling techniques can be used with or without static checking. The modeling problem is orthogonal to static typing, so regardless of your feelings about static checking, you should recognize the intrinsic value in each of these techniques.

Class Modeling


You know all about this one. Class-based OO design is the 800-pound gorilla of domain modeling these days. Its appeal is that it's a natural match for the way we already model things in everyday life. It can take a little practice at first, but for most people class modeling quickly becomes second nature.

Although the industry loves OO design, it's not especially well liked as an academic topic. This is because OO design has no real mathematical foundation to support it — at least, not until someone comes along and creates a formal model for side effects. The concepts of OOP stem not from mathematics but from fuzzy intuition.

This in some sense explains its popularity, and it also explains why OOP has so many subtly different flavors in practice: whether (and how) to support multiple inheritance, static members, method overloading vs. rich signatures, and so on. Industry folks can never quite agree on what OOP is, but we love it all the same.

Relational Modeling


Relational database modeling is a bit harder and takes more practice, because its strength stems from its mathematical foundation. Relational modeling can be intuitive, depending on the problem domain, but most people would agree that it is not necessarily so: it takes some real skill to learn how to model arbitrary problems as relational schemas.

Object modeling and relational modeling produce very different designs, each with its strengths and weaknesses, and one of the trickiest problems we face in our industry has always been the object-relational mapping (ORM) problem. It's a big deal. Some people may have let you to believe that it's simple, or that it's automatically handled by frameworks such as Rails or Hibernate. Those who know better know just how hard ORM is in real-world production schemas and systems.

XML Modeling


XML provides yet another technique for modeling problems. Usually XML is used to model data, but it can also be used to model code. For instance, XML-based frameworks such as Apache Ant and XSLT offer computational facilities: loops or recursion, conditional expressions and setting variables.

In many domains, programmers will decide on an XML representation before they've thought much about the class model, because for those domains XML actually offers the most convenient way of thinking about the problem.

The kinds of data that work well with XML modeling tend to be poorly suited for relational modeling, and vice-versa, with the practical result that XML/relational mapping is almost as infamously thorny as O/R mapping.

And as for XML/OO mapping, most of us tend to treat it as a more or less solved problem. However, in practice there are several competing ways of doing XML/OO mapping. The W3C DOM and SAX enjoy the broadest use, but they are both sufficiently cumbersome that alternatives such as JDom and REXML (among others) have gained significant followings.

I mention this not to start a fight, but only to illustrate that XML is a third modeling technique in its own right. It has both natural resonances and surfaces of friction with both relational design and OO design, as one might expect.

Other schools


I'm not claiming that these three modeling schools are the only schools out there – far from it! Two other obvious candidates are Functional modeling (in the sense of Functional Programming, with roots in the lambda calculus) and Prolog-style logical modeling. Both are mature problem-modeling strategies, each with its pros and cons, and each having varying degrees of overlap with other strategies. And there are still other schools, perhaps dozens of them.

The important takeaway is that none of these modeling schools is "better" than its peers. Each one can model essentially any problem.

There are tradeoffs involved with each school, by definition — otherwise all but one would have disappeared by now.

Finding the sweet spot


Sometimes it makes sense to use multiple modeling techniques in the same problem space. You might do a mixed XML/relational data design, or a class-based OO design with Functional aspects, or embed a rules engine in a larger system.

Choosing the right technique comes down to convenience. For any given real-world problem, one or two modeling schools are likely to be the most convenient approaches. Exactly which one or two depends entirely on the particulars of the problem.

By convenient, I mean something different from what you might be thinking. To me, a convenient design is one that is convenient for the users of the design. And it should also be convenient to express, in the sense of minimalism: all else being equal, a smaller design beats a big one. One way of looking at this is that the design should be convenient for itself!

Unfortunately, most programmers (myself included) tend to use exactly the wrong definition of convenience: they choose a modeling technique that is convenient for themselves. If they only have experience in one or two schools, guess which techniques they'll jump to for every problem they face?

This problem rears its head throughout computing. There's always a "best" tool for any job, but if programmers don't know how to use it, they'll choose an inferior tool because they think their schedule doesn't permit a learning curve. In the long run they're hurting their schedules, but it's hard to see that when you're down in the trenches.

Modeling schools are just like programming languages, web frameworks, editing environments and many other tools: you won't know how to pick the right one unless you have a reasonably good understanding of all of them, and preferably some practice with each.

The important thing to remember is that all modeling schools are "first class" in the sense of being able to represent any problem, and no modeling school is ideal for every situation. Just because you are most comfortable solving a problem using a particular strategy does not mean that it is the ideal solution to the problem. The best programmers aim to master all available techniques, giving them a better chance at making the right choices.

Property Modeling


With this context in mind, I claim that the Properties Pattern is yet another kind of domain modeling, with its own unique strengths and tradeoffs, distinct from all the other modeling schools I've mentioned. It is their first-class peer, inasmuch as it is capable of modeling the same broad set of problem domains.

After we've finished talking about the Properties Pattern in exhausting detail, I think I'll have convinced you of the pattern's status as a major school of modeling. Hopefully you'll also start to have a feel for the kinds of problems it's well-suited to solve – sometimes more so than other schools, even your current favorite.

But before we dive into technical details, let's take a brief peek at a fascinating comparison of Property-based modeling to class-based OO design. It's a non-technical argument that I think has some real force behind it.

Brains and Thoughts


Douglas Hofstadter has spent a lifetime thinking about the way we think. He's written about it perhaps more than anyone else in the past century. Even if someone out there has beaten him in sheer quantity of words on the subject, nobody has come close to rivaling his style or his impact on programmers everywhere.

All of his books are wonderfully imaginative and are loads of fun to read, but if you're a programmer and you haven't yet read Gödel, Escher, Bach: An Eternal Golden Braid (usually known as "GEB"), then I envy you: you're in for a real treat. Get yourself a copy and settle in for one of the most interesting, maddening, awe-inspiring and just plain fun books ever written. The Pulitzer Prize it won doesn't nearly do it justice. It's one of the greatest and most unique works of imagination of all time.

Hofstadter made a compelling argument in GEB (thirty years ago!) that property-based modeling is fundamental to the way our brains work. In Chapter XI ("Brains and Thoughts"), there are three little sections titled Classes and Instances, The Prototype Principle, and The Splitting-off of Instances from Classes that together form the conceptual underpinnings of the Properties Pattern. In these little discussions Hofstadter explains how the Prototype Principle relates to classic class-based modeling.

I wish I could reproduce his discussion in full here — it's only three pages — but I'll have to just encourage you to go read it instead. His thesis is this:
The most specific event can serve as a general example of a class of events.

Hofstadter offers several supporting examples for this thesis, but I'll paraphrase one of my all-time favorites. It goes more or less as follows.

Imagine you're listening to announcers commenting on an NFL (American football) game. They're talking about a new rookie player that you don't know anything about. At this point, the rookie – let's say his name is L.T. – is just an instance of the class "football player" with no differentiation.

The announcers mention that L.T. is a running back: a bit like Emmitt Smith in that he has great speed and balance, and he's great at finding holes in the defense.

At this point, L.T. is basically an "instance" of (or a clone of) Emmitt Smith: he just inherited all of Emmitt's properties, at least the ones that you're familiar with.

Then the announcers add that L.T. is also great at catching the ball, so he's sometimes used as a wide receiver. Oh, and he wears a visor. And he runs like Walter Payton. And so on.

As the announcers add distinguishing attributes, L.T. the Rookie gradually takes shape as a particular entity that relies less and less on the parent class of "football player". He's become a very, very specific football player.

But here's the rub: even though he's a specific instance, you can now use him as a class! If Joe the Rookie comes along next season, the announcers might say: "Joe's a lot like L.T.", and just like that, Joe has inherited all of L.T.'s properties, each of which can be overridden to turn Joe into his own specific, unique instance of a football player.

This is called prototype-based modeling: Emmitt Smith was a prototype for L.T., and L.T. became a prototype for Joe, who in turn can serve as the prototype for someone else. Hofstadter says of The Prototype Principle:

"This idea that there is generality in the specific is of far-reaching importance."


Again, it's a three-page discussion that I've just skimmed here. You should go read it for yourself. Heck, you should read the whole book: it's one of the greatest books ever written, period, and every programmer ought to be familiar with it.

Hopefully my little recap of Hofstadter's argument has convinced you that my calling it the "Universal Design Pattern" might just possibly be more than a marketing trick to get you to read my blog, and that the rest of this article is worth a look.

The Properties Pattern is unfortunately big enough to deserve a whole book. Calling an entire school of modeling a "design pattern" is actually selling it short by a large margin.

Hence, if this article seems excruciatingly long, it's because I've tried to cram a whole book into a blog, as I often do. But look on the bright side! I've saved you a bunch of time this way. This will go much faster than reading a whole book.

Even so, don't feel bad if it takes a few sittings to get through it all. It's still a lot of information. I considered splitting it into 3 articles, but instead I just cut about half of the material out. (Jeff and Joel: seriously. I cut 50%.)

Who uses the Properties Pattern?


I assume I've already convinced you that this pattern is worth learning about, or you'd have left by now. I'm showing you these use cases not to draw you in, but to show you some of the very different ways the pattern can be used.

We could probably find hundreds of examples, but I'll focus on just a handful of real-world uses that I hope will illustrate just how widespread and flexible it is.

Before we start, there are two things to keep in mind. The first is that people have different names for this pattern, because even though it's quite commonplace, there hasn't been much literature on it. One paper calls it Do-It-Yourself Reflection. Another article calls it Adaptive Object Modeling. See Further reading for the few links I could dig up.

Whatever name you use, once you know how to look for it, you'll start seeing this pattern everywhere, wearing various disguises. Now that we have a common name for it, it should be easier to spot in the wild.

The second thing to keep in mind is that the Properties Pattern scales up: you can choose how much to use it in your system. It can be anything from simple property lists attached to a few of your classes to make them user-annotatable, up through a full-fledged prototype-based framework that serves as the foundation for modeling everything in your system.

So our examples will range from small ones to very big ones.

Eclipse


One nice small-scale example of the pattern is the Eclipse Java Development Tools (JDT): a set of classes that model the Java programming language itself, including the abstract syntax tree, the symbol graph and other metadata. This is used by the Eclipse backend to do all the neat magic it does with your Java code, by treating Java source code as a set of data structures.

You can view the javadoc for this class hierarchy at help.eclipse.org. Click on JDT Plug-in Developer Guide, then Programmer's Guide, then JDT Core, then org.eclipse.jdt.core.dom. This package defines strongly-typed classes and interfaces that Eclipse uses for modeling the Java programming language itself.

If you click through any class inheriting from ASTNode you'll see that it has a property list. ASTNode's javadoc comment says:
"Each AST node is capable of carrying an open-ended collection of client-defined properties. Newly created nodes have none. getProperty and setProperty are used to access these properties."

I like this example for several reasons. First, it's a very simple use of the Properties pattern. It doesn't muck around with prototypes, serialization, metaprogramming or many of the other things I'll talk about in a little bit. So it's a good introduction.

Second, it's placed smack in the middle of a very, very strongly-typed system, showing that the Properties pattern and conventional statically-typed classed-based modeling are by no means mutually exclusive, and can complement one another nicely.

And third, their property system itself is fairly strongly typed: they define a set of support classes such as StructuralPropertyDescriptor, SimplePropertyDescriptor, and ChildListPropertyDescriptor to help place some constraints on client property values. I'm not a huge fan of this approach myself, since I feel it makes their API fairly heavyweight. But it's a perfectly valid stylistic choice, and it's useful for you to know that you can implement the pattern this way if you so choose.

JavaScript


At the other end of the "how far to go with it" spectrum we have the JavaScript programming language, which places the Prototype Principle and Properties Pattern at the very core of the language.

People love to lump dynamic languages together, and they'll often write off JavaScript as some sort of inferior version of Perl, Python or Ruby. I was guilty of this myself for over a decade.

But JavaScript is substantively different from most other dynamic languages (even Lisp), because it has made the Properties Pattern its central modeling mechanism. It borrowed this heritage largely from a language called Self, and some other modern languages (notably Io and one other language that I'll talk about below) have also chosen prototypes and properties over traditional classes.

In JavaScript, every user-interactible object in the system inherits from Object, which has a built-in property list. Prototype inheritance (think back to our example of the Emmitt Smith instance having been the prototype for the L.T. instance) is a first-class language mechanism, and JavaScript offers several kinds of syntactic support for accessing properties and declaring property lists (as "object literals").

JavaScript is often accurately described as the world's most misunderstood programming language. Armed with our newfound knowledge, we can start to see JavaScript in a new light. To use JavaScript effectively, you need to gain experience with a whole new School of Modeling. If you simply try to use JavaScript as a substitute for (say) Java or Python, you'll encounter tremendous friction.

Since most of us have precious little actual experience with property-based modeling, this is exactly what happens, and it's no wonder JavaScript gets a bad rap.

Pushing it even further


In addition to how centrally you want to use the Properties pattern in your system, you can also decide how recursive to make it: do your properties have explicit meta-properties? Do you have metaprogramming hooks? How much built-in reflection do you offer?

JavaScript offers a few metaprogramming hooks. One such hook is the recently-introduced __noSuchMethod__, which lets you intercept a failed attempt to invoke a nonexistent function-valued property on an object.

Unfortunately JavaScript does not offer as many hooks as I'd like. For instance, there is no corresponding __noSuchField__ hook, which limits the overall flexibility somewhat. And there are no standard mechanisms for property-change event notification, nor any reasonable way to provide such a mechanism. So JavaScript gets it mostly right, but it stops short, possibly for performance reasons, of offering a fully-extensible metaprogramming system such as those offered by SmallTalk and to some extent, Ruby.

The pattern takes shape...


Before we move on to other uses of the Property Pattern, let's put JavaScript (and its central use of the pattern) into perspective, by comparing it to another successful language.

First: JavaScript is not my favorite language. I've done a lot of JavaScript programming over the past 2 years or so, both client-side and server-side, so I'm as familiar with it as I am with any other language I've used.

JavaScript in its current incarnation is not the best tool for many tasks. For instance, it's not great for building APIs, and it's not great for Unix scripting the way Perl and Ruby are. It has no library or package system, no namespaces, and is missing many other modern conveniences. If you're looking for a general-purpose language, JavaScript leaves you wanting.

But JavaScript is the best tool for many other tasks. As just one example, JavaScript is an outstanding language for writing unit tests — both for itself, and also for testing code in other languages. Being able to use the Properties Pattern to treat every object (and class) as a bag of properties makes the creation of mock objects a dream come true. The syntactic support for object literals makes it even better. You don't need any of the silly frameworks you see coming from Java, C++ or even Python.

And JavaScript is one of the two best scripting languages on the planet, in the most correct sense of the term "scripting language": namely, languages that were designed specifically to be embedded in larger host systems and then used to manipulate or "script" objects in the host system. This is what JavaScript was designed to do. It's reasonably small with some optional extensions, it has a reasonably tight informal specification, and it has a carefully crafted interface for surfacing host-system objects transparently in JavaScript.

In contrast, Perl, Python and Ruby are huge sprawls, all trying (like C++ and Java) to be the best language for every task. The only other mainstream language out there that competes with JavaScript for scripting arbitrary host systems is Lua, famous for being the scripting language of choice for the game industry.

And wouldn't you know it, Lua is also a language that uses the Properties Pattern as its central design. Its central Table structure is remarkably similar to JavaScript's built-in Object, and Lua also uses prototypes rather than classes.

So the world's two most successful scripting languages are prototype-based systems. Is this just a cosmic coincidence? Or is it possible that a suitably designed class-based language could have been just as successful?

It's hard to say. I've used Jython as an embedded scripting language for a long time, and it's worked pretty well. But I've personally come to believe that the Properties Pattern is actually better suited for extensibility than class-based modeling, and that prototype-based languages make better extension languages than class-based languages. That's effectively what's happening with embedded scripting: the end-users are growing and extending the host system.

In fact I was convinced of it before I even knew JavaScript. Let's take a look at another interesting "Who uses it?" example: Wyvern.

Wyvern


My multiplayer game Wyvern takes the Properties Pattern quite far as well, although in some different directions than what we've discussed so far. I designed Wyvern long before I'd heard of Self or Lua, and before I'd learned anything about JavaScript. In retrospect it's amazing how similar my design was to theirs.

Wyvern is implemented in Java, but the root GameObject class has a property list, much like JavaScript's Object base class. Wyvern has prototype inheritance, but since I'd never heard of prototypes before, I called them archetypes. In Wyvern, any game object can be the archetype for any other game object, and property lookup and inheritance work more or less identically to the way they work in JavaScript.

I arrived at this design after scratching my head for months (in late 1996) over how to build the ultimate extensible game. I wanted all the game content to be created by players, and I came up with dozens upon dozens of detailed use cases, in all of which I wanted players to be able to extend the game functionality in surprising new ways. In the end I arrived at a set of interleaved design patterns, including a rich command system, a rich hooks/advice system, and several other subsystems I'd love to document someday.

But the core data model was the Properties Pattern.

In some ways, Wyvern's implementation is more full-featured than JavaScript's. Wyvern offers more metaprogramming facilities, such as vetoable property change notifications, which gives in-game objects tremendous flexibility in responding to their environment. Wyvern also supports both transient and persistent properties, a scheme I'll discuss below.

On other ways, Wyvern just made different decisions. One big one is that Wyvern's property values are statically typed. The property names are always strings, just like in JavaScript, but the values can be various leaf types (ints, longs, booleans, strings, etc.), or functions (a trick that wasn't easy in Java), or even archetypes.

But despite the differences, Wyvern's core property-list infrastructure is a lot like that of JavaScript, Self and Lua. And it's been a design I've been fundamentally happy with for over ten years. It's met or exceeded all my original expectations for enabling end-user extensibility, particularly in its ability to let people extend the in-game behavior on the fly, without needing to reboot. This has proven extraordinarily powerful (and popular with the players.)

Where Wyvern clearly got the pattern wrong was in its lack of support for syntax. As soon as I decided to use the Properties pattern centrally in my game, I should have decided to use a programming language better suited for implementing the pattern: ideally, one that supports it from the ground up.

I eventually wound up using Python (actually, Jython) for a ton of my code, and it was far more succinct and flexible than anything I wrote in Java. But I was foolishly worried about performance, and as a result I wound up writing at least half the high-level game logic in Java and piling on hundreds of thousands of lines of getProperty and setProperty code. And now the system is hard to optimize; it would have been much easier if I'd had a cleaner separation of game-engine infrastructure from "scripty" game code.

Even if I'd done the whole game in Python, I'd still have had to implement a prototype inheritance framework to enable any object to be able to serve as the prototype for any other object.

I realize I haven't really explained why prototype inheritance works so well, except for my brief mention of mock objects for unit testing. But to keep this article tractable, I had to delete several pages of detailed examples, such as "Chieftain Monsters" that could be programmatically constructed by adding a few new properties to any existing monster

When I told you this pattern was big enough for a book, I meant a big book. Without the examples handy, all I can do is say that using JavaScript/Rhino (or Lua, once it became available on the JVM) might have made my life easier. Or heck, writing my own language might have been the best choice for a system that large and ambitious.

In any case, live and learn. It's a lot of code, but Wyvern is still a properties-based, prototype-based system, and it has amazing open-ended flexibility as a result.

We've been through the two big examples now (Wyvern and JavaScript). I'll close this "Who Uses It" section with just a few more key examples.

Lisp


Lisp features a small-scale example of the Properties Pattern: it has property lists for symbols. Symbols are first-class entities in Lisp. They're effectively the names in your current namespace, like Java's fully-qualified class names.

If Java classes all had property lists, it would still be a small-scale instantiation of the Properties pattern, but it would open up an awful lot of new design possibilities to Java programmers. Similarly, Lisp stops short of making everything have a property list, but to the extent it offers property lists they're exceptionally useful design tools.

Emacs Lisp actually makes heavy use of the Properties Pattern, inasmuch as essentially every one of its thousands of configuration settings is a property in the global namespace. It supports the notion of transient vs. persistent properties, and it offers a limited form of property inheritance via its buffer-local variables.

Unfortunately Emacs doesn't support any notion of prototypes, and in fact it doesn't have any object-orientation facilities at all. Sometimes I want to model things in Emacs using objects with flexible property lists, and at such times I find myself wishing I were using JavaScript. But even without prototypes, Emacs gains significant extensibility from its use of properties for data representation.

Keep in mind that there are, of course, big tradeoffs to make when you're deciding how much to use the Properties pattern; I'll discuss them in a bit. I'm not criticizing any of the systems or languages here for the choices they've made; all of them have been improved by their use of this pattern, regardless of how far they decided to take it.

XML revisited


Earlier I described XML as a first-class modeling school. Now that we have more context, it's possible to view XML as being an instantiation of the Properties Pattern, inasmuch as it uses the pattern as part of its fundamental structure.

XML's view of the pattern is two-dimensional: properties can take the form of either attributes or elements, each kind having different syntactic and semantic restrictions. Many folks have criticized XML for the unnecessary complexity of this redundant pair of property subsystems, but in the end it doesn't really matter much, since two ways to model properties is still better than zero ways.

So far we've seen various policies around static checking: Eclipse (strong/mandatory), JavaScript/Lua (very little), and Wyvern (moderate).

XML offers what I think is the ideal policy, which is that it lets you decide for yourself. During your initial domain modeling (the "prototyping" phase — a term now loaded with Even More Delicious Meaning), you can go with very weak typing, opting for nothing more than simple well-formedness checks. And for many problems, this is as much static checking as you'll ever need, so it's nice that you have this option.

As some of your models become more complex, you can choose to use a DTD for extra validation. And if you need a really heavy-duty constraint system, you can migrate up to a full-fledged XML Schema or Relax NG schema, depending on your needs.

XML has proven to be a very popular modeling tool for Java programmers in particular — more so than for the dynamic language communities. This is because Java offers essentially zero support for the Properties Pattern. When Java programmers need access to the pattern, the easiest approach is currently to use XML.

The Java/XML combination has proven reasonably powerful, despite the lack of syntactic integration and numerous other impedance mismatches. Using XML is still often preferable to modeling things with Java classes. Even Eclipse's AST property lists might have been better modeled using XML and a DOM: it would have been less work, and the interface would have been more familiar. And as for Apache Ant: JSON-style JavaScript objects for build files would have been exactly what they needed, but by the time they'd realized they needed a plug-in system, the damage was done.

As Mozilla Rhino becomes better documented, and as more Java programmers begin to appreciate the usefulness of JSON as a lightweight alternative to XML, JavaScript may begin to close the gap. Rhino provides Java with the Properties Pattern much more seamlessly than any XML solution. I've already mentioned that it's superior (even to XML) for unit tests and representing mock test data.

But it goes deeper than unit testing. Every sufficiently large Java program, anything beyond medium-sized, needs a scripting engine, whether the authors realize it or not. Programs often have to grow to the size of browsers or spreadsheets or word processors before the authors finally realize they need to offer scripting facilities, but in practice, even small programs can immediately benefit from scripting. And XML doesn't fit the bill. It's yet another example of programmers choosing a School of Modeling because they know it, rather than learning how to use the right tool for the job.

So it goes.

Bigtable


Last example: Google's Bigtable, which provides a massively scalable, high performance data store for many Google applications (some of which are described in the paper – click the link if you're curious.) This particular instantiation of the Properties Pattern is a multidimensional table structure, where the keys are simple strings, and the leaf values are opaque blobs.

Hardcore relational data modelers will sometimes claim that large systems will completely degenerate in the absence of strong schema constraints, and that such systems will also fail to perform adequately. Bigtable provides a nice counterexample to these claims.

That said, explicit schemas are useful for many domains, and I'll talk more about how they relate to the Properties Pattern in a bit.

This would probably be a good time to mention Amazon's Simple Storage Service, but I don't know anything about it. I've heard they use name-value pairs.

In any case, I hope these examples (Eclipse AST classes, JavaScript, Wyvern game objects, Lisp symbols, XML and HTML, and Bigtable) have convinced you that the Properties pattern is ubiquitous, powerful, and multifaceted, and that it should be part of any programmer or designer's lineup.

Let's look in more depth at how it's implemented, its trade-offs, and other aspects of this flexible design strategy.

Properties Pattern high-level overview


At a high level, every implementation of the Properties Pattern has the same core API. It's the core API for any collection that maps names to values:
  • get(name)
  • put(name, value)
  • has(name)
  • remove(name)
There are typically also ways to iterate over the properties, optionally with a filter of some sort.

So the simplest implementation of the Properties Pattern is a Map of some sort. The objects in your system are Maps, and their elements are Properties.

The next step in expressive power is to reserve a special property name to represent the (optional) parent link. You can call it "parent", or "class", or "prototype", or "mommy", or anything you like. If present, it points to another Map.

Now that you have a parent link, you can enhance the semantics of get, put, has and remove to follow the parent pointer if the specified property isn't in the object's list. This is largely straightforward, with a few catches that we'll discuss below. But you should be able to envision how you'd do it without too much thought.

At this point you have a full-fledged Prototype Pattern implementation. All it took was a parent link!

From here the pattern can expand in many directions, and we'll cover a few of the interesting ones in the remainder of this article.

Representations


There are two main low-level implementation considerations: how to represent property keys, and what data structure to use for storing the key/value pairs.

Keys


The Properties pattern almost always uses String keys. It's possible to use arbitrary objects, but the pattern becomes more useful with string keys because it trivially enables prototype inheritance. (It's tricky to "inherit" a property whose key is some opaque blob - we usually think of inheritance as including a set of named fields from the parent.)

JavaScript permits you to use arbitrary objects as keys, but what's really happening under the covers is that they're being cast to strings, and they lose their unique identity. This means JavaScript Object property lists cannot be used as be a general-purpose hashtable with arbitrary unique objects for keys.

Some systems permit both strings and numbers as keys. If your keys are positive integers, then your Map starts looking an awful lot like an Array. If you think about it, Arrays and Maps share the same underlying formalism (a surjection, not to put too fine a point on it), and in some languages, notably PHP, there isn't a user-visible difference between them.

JavaScript permits numeric keys, and allows you to specify them as either strings or numbers. If your object is of type Array, you can access the numeric keys via array-indexing syntax.

Quoting


JavaScript syntax is especially nice (compared to Ruby and Python) because it allows you to use unquoted keys. For instance, you can say
var person = {
name: "Bob",
age: 20,
favorite_days: ['thursday', 'sunday']
}
and the symbols name, age and favorite_days are NOT treated as identifiers and resolved via the symbol table. They're treated exactly as if you'd written:
var person = {
"name": "Bob",
"age": 20,
"favorite_days": ['thursday', 'sunday']
}
You also have to decide whether to require quoting values. It can go either way. For instance, XML requires attribute values to be quoted, but HTML does not (assuming the value has no whitespace in it).

Missing keys


You will need to decide how to represent "property not present". In the simplest case, if the key isn't in the list, the property is not there (but see Inheritance further on).

If a property is frequently removed and re-added, it may make sense to leave the key in the list with a null value. In some systems, you may need null to be a valid property value, in which case you'd need to use some other distinguished (and reserved) value for this micro-optimization to work.

Data structures


The simplest property-list implementation is a linked list. You can either have the alternating elements be the keys and values (Lisp does this), or you can have each element be a struct containing pointers to the key and value.

The linked list implementation is appropriate when:
  • you're just using the pattern to allow user annotations on object instances
  • you don't expect many such annotations on any given instance
  • you're not incorporating inheritance, serialization or meta-properties into your use of the pattern
Logically a property list is an unordered set, not a sequential list, but when the set size is small enough a linked list can yield the best performance. The performance of a linked list is O(N), so for long property lists the performance can deteriorate rapidly.

The next most common implementation choice is a hashtable, which yields amortized constant-time find/insert/remove for a given list, albeit at the cost of more memory overhead and a higher fixed per-access cost (the cost of the hash function.)

In most systems, a hashtable imposes too much overhead when objects are expected to have only a handful of properties, up to perhaps two or three dozen. A common solution is to use a hybrid model, in which the property list begins life as a simple array or linked list, and when it crosses some predefined threshold (perhaps 40 to 50 items), the properties are moved into a hashtable.

Note that we'll often refer to property sets as "property lists" (or "plists" for short), because they're so often implemented as lists. But it's fairly unusual for the order to matter. In the rare cases when it matters, there are usually two possibilities: the names need to be kept in insertion order, or they need to be sorted.

If you need constant-time access and want to maintain the insertion order, you can't do better than a LinkedHashMap, a truly wonderful data structure. The only way it could possibly be more wonderful is if there were a concurrent version. But alas.

If you need to impose a sort order on property names, you'll want to use an ordered-map implementation, typically an ordered binary tree such as a splay tree or red/black tree. A splay tree can be a good choice because of the low fixed overhead for insertion, lookup and deletion, but with the tradeoff that its theoretical worst-case performance is that of a linked list. A splay tree can be especially useful when properties are not always accessed uniformly: if a small subset M of an object's N properties are accessed most often, the amortized performance becomes O(log M), making it a bit like an LRU cache.

Note that you can get a poor-man's splay tree (at least, the LRU trick of bubbling recent entries to the front of the list) using a linked list by simply moving any queried element to the front of the list, a constant-time operation. It's surprising that more implementations don't take this simple step: an essentially free speedup over the lifetime of most property lists.

Inheritance


With prototype inheritance, each property list can have a parent list. When you look for a property on an object, first you check the object's "local" property list, and then you look in its parent list, on up the chain.

As I described in the Overview, the simplest approach for implementing inheritance is to set aside a name for the property pointing to the parent property list: "prototype", "parent", "class" and "archetype" are all common choices.

It's unusual (but possible) to have a multiple-inheritance strategy in the Properties pattern. In this case the parent link is a list rather than a single value, and it's up to you to decide the rules for traversing the parent chains during lookups.

The algorithm for inherited property lookup is simple: look in my list, and if the property isn't there, look in my parent's list. If I have no parent, return null. This can be accomplished recursively with less code, and but it's usually wiser to do it iteratively, unless your language supports tail-recursion elimination. Property lookups can be the most expensive bottleneck in a Properties Pattern system, so thinking about their performance is (for once) almost never premature.

The deletion problem


If you delete a property from an object, you usually want subsequent checks for the property to return "not found". In non-inheritance versions of the pattern, to delete a property you simply remove its key and value from the data structure.

In the presence of inheritance the problem gets trickier, because a missing key does not mean "not found" – it means "look in my parent to see if I've inherited this property."

To make the problem clearer, assume you have a prototype list called Cat with a property named "friendly-to-dogs", whose value defaults to the boolean true. Let's say you have a specific cat instance named Morris, whose prototype is Cat:
var Cat = {
friendly_to_dogs: true
}

var Morris = {
prototype: Cat
}
Let's say Morris has a nasty run-in with a dog, and now he hates all dogs, so we want to make a runtime update to his friendly-to-dogs property. Our first idea might be to delete the property, since a missing key or null value are often interpreted as false in a boolean context. (This is true even in class-based languages like C++ or Java, in which a hasFooBar function will return true if the internal fooBar field is non-null.)

However, Morris does not have a copy of "friendly-to-dogs" in his local list: he inherits it from Cat. So if your deleteProperty method does nothing but delete the property from the local list, he will continue to inherit "friendly-to-dogs", which will irk him (and you) endlessly until you figure out where the bug is.

You can't delete "friendly-to-dogs" from the Cat property list, or all of your cats will suddenly become dog-haters, and you'll have outright war on your hands. (Note that in some settings this is exactly what you want to do, illustrating the inherent universal trade-off between flexibility and safety.)

The solution for Morris is to have a special "NOT_PRESENT" property value that deleteProperty sets when you delete a property that would otherwise be inherited. This object should be a flyweight value so that you can check it with a pointer comparison.

So to account for deletion of inherited properties, we have to modify our property-lookup algorithm to look in the local list for (a) a missing key, (b) a null value, or (c) the NOT_PRESENT tag. If any of these apply, the property is considered not present on the object. [Note: the semantics of null values are up to the system designer. You don't have to make null values mean "not there." Either way is fine.]

Read/write asymmetry


One logical consequence of prototype inheritance as we've defined it is that reads and writes work differently. In particular, if you read an inherited property, it gets the value from an ancestor in the prototype chain. But if you write an inherited property, it sets the value in the object's local list, not in the ancestor.

To illustrate, let's add a "night-vision" property to our Cat prototype. Its value is expected to be an integer representing how well the cat can see in the dark. Let's say that the default value is 5, but our hero Morris has been eating his carrots, so we want to set his "night-vision" property value to 7.

The setProperty code does not need to check the parent chain: it simply adds the key/value pair {"night-vision", 7} to Morris's local property list. If we set the property on Cat, then all cats would have Morris's super-vision, which isn't what we want.

This asymmetry is normal. Back in our L.T. / Emmitt Smith example, when we were adding properties to L.T., we didn't want to modify Emmitt! It's just how the pattern works: you override inherited values by adding local properties, even when the override is a deletion.

Read-only plists


Many implementations of the pattern offer "frozen" property lists. Sometimes (e.g. for debugging) it's useful to flag an entire property list as read-only. Ruby supports this via the "freeze" method on the built-in root Object class. In any sufficiently large, robust implementation of the Properties pattern, you should include the option to freeze your property lists.

If you offer a "freeze" function, you should think about whether you want to offer a "thaw" as well. The decision depends on whether you want to offer programmers additional protection, or you just want to lock them up and throw away the key.

My personal view is that Java programmers tend to overuse the "freeze" function when they start with Ruby. For that matter, they tend to overuse "final" in Java. I mentioned before the trade-off between flexibility and safety. When you use the Properties Pattern, you're consciously choosing flexibility over safety, and in many domains this is the right choice. In fact, safety can be viewed as a kind of optimization: something that should ideally be layered on, functioning behind the scenes rather than being interleaved with the user APIs and flexible data model.

A nice (and simple to implement) compromise on safety and flexibility is to offer a ReadOnly property attribute, as JavaScript does. There are certain properties (such as the parent pointer) that are less likely to need to change as the system evolves, so it's probably OK to lock them down early on. Doing this on a property-by-property basis is much less draconian. Even better, you should consider making the ReadOnly property attribute non-inheritable, so that subtypes can choose their own policies without compromising the integrity of the supertypes.

We're more or less done with inheritance: it's not very complicated. There are a few other inheritance-related design issues that I'll cover in upcoming sections.

Performance


Performance is one of the biggest trade-offs of using the Properties Pattern. Many engineers are so concerned with performance (and its attendant paradoxes and fallacies) that they refuse to consider using the Properties pattern, regardless of the situation.

As it happens, the pattern's performance can be improved and mitigated in several clever ways. I won't cover all of them here, but I'll touch on some of the classics and one or two new approaches.

Interning strings


Make sure your string keys are interned. Most languages provide some facility for interning strings, since it's such a huge performance win. Interning means replacing strings with a canonical copy of the string: a single, immutable shared instance. Then the lookup algorithm can use pointer equality rather than string contents comparison to check keys, so the fixed overhead is much lower.

The only downside of interning is that it doesn't help much when you're constructing a property name on the fly, since you still need to hash the string to intern it.

That's not much of a downside, so as a rule, you should always intern your keys. A large percentage of property names in any system are accessed as string literals from the source code (or are read from a configuration file and can be interned all at once when the file is read), and interning works in these common cases.

Corollary: don't use case-insensitive keys. It's performance suicide. Case-insensitive string comparison is really slow, especially in a Unicode environment.

Perfect hashing


If you know all the properties in a given plist at compile-time (or at runtime early on in the life of the process), then you might consider using a "perfect hash function generator" to create an ideal hash function just for that list. It's almost certainly more work than it's worth unless your profiler shows that the list is eating a significant percentage of your cycles. But such generators (e.g. gperf) do exist, and are tailor-made for this situation.

Perfect hashing doesn't conflict with the extensible-system nature of the Properties pattern. You may have a particular set of prototype objects (such as your built-in monsters, weapons, armor and so on) that are well-defined and that do not typically change during the course of a system session. Using a perfect hash function generator on them can speed up lookups, and then if any of them is modified at runtime, you just fall back to your normal hashing scheme for that property list.

Copy-on-read caching


If you have lots of memory, and your leaf objects are inheriting from prototype objects that are unlikely to change at runtime, you might try copy-on-read caching. In its simplest form, whenever you read a property from the parent prototype chain, you copy its value down to the object's local list.

The main downside to this approach is that if the prototype object from which you copied the property ever changes, your leaf objects will have the now-incorrect old value for the property.

Let's call copy-on-read caching "plundering" for this discussion, for brevity. If Morris caches his prototype Cat's copy of the "favorite-food" property (value: "9Lives"), then Morris is the "plunderer" and Cat is the plundered object.

The most common workaround to the stale-cache problem is to keep a separate data structure mapping plundered objects to their plunderers. It should use weak references so as not to impede garbage collection. (If you're writing this in C++, then may God have mercy on your soul.) Whenever a plundered object changes, you need to go through the plunderers and remove their cached copy of the property, assuming it hasn't since then changed from the original inherited value.

That's a lot of stuff to keep track of, so plundering is a strategy best used only in the direst of desperation. But if performance is your key issue, and nothing else works, then plundering may help.

Refactoring to fields


Another performance speedup technique is to take your N most commonly used properties and turn them into instance variables. Note that this technique is only available in languages that differentiate between instance variables and properties, so it would work in Java but not in JavaScript.

This optimization may sound amazingly attractive, especially during your first round of performance optimizations. Be warned: this approach is fraught with pitfalls, so (as with nearly all performance optimizations) you should only use it if your profiler proves that the benefits will outweigh the costs.

The first cost is API incompatibility: suddenly instead of accessing all properties uniformly through a single getProperty/setProperty interface, you now have specific fields that have their own getters and setters, which could potentially have massive impact in your system (since, after all, these are the most commonly-accessed properties). And unless you're using Emacs, your refactoring editor probably isn't smart enough to do rename-method constrained on argument value.

You can mitigate the API problem by continuing to go through the get/setProperty interface, and have them check the argument to see if it's one of the hardwired fields. This will result in an increasingly large switch-statement (or equivalent), so you're trading API code maintenance for API simplicity. It also slows down the field access considerably, which offsets the performance gain from using a field.

The next cost is system complexity: you have twice as many code paths through every part of your system that deals with the Properties pattern. Does inheritance still work the same? What about serialization? Transient properties? Metaprogramming? What about your user interface for accessing and modifying property lists? You face a huge code-bloat problem when you split property access into two classes: plist properties and instance variables.

The next cost is accidentally getting it wrong: how do you know what the most-accessed properties are? You may do some runtime profiling and see that it's one set, but over time the characteristics of your system might change in such a way that it's an entirely different set. Realistically you will have to instrument your system to keep track, on a regular basis, of which properties are accessed at a rate beyond your tolerance threshold, so you can convert them to fields as well. This isn't a one-off optimization.

But all these costs pale in comparison to the big one, which is extensibility: instance variables are set in stone. It will be a vast amount of work to try to give them parity with your plist properties: change-list notifications, the ability to override them or remove them, and so on. It's likely that you will wind up sacrificing at least some flexibility for these fields.

So use this optimization with extreme caution.

Refrigerator


The last performance optimization I'll mention is more about conserving memory than CPU. If you're worried about the overhead of a per-object property-list field, even if it's usually null, then you can implement property lists using a separate, external data structure.

I don't know what it's normally called, so I'm calling it the Refrigerator, since you're basically putting yellow stickies all over it. The idea is that you don't need to pay for the overhead of property lists when very few of the objects in your system will ever have one. Instead of using a field in each class with a property list, you maintain a global hashtable whose keys are object instances, and whose values are property lists.

To fetch the property list of an object, you go look to see if it's on the Refrigerator. The property list itself can follow any of the implementation schemes I discussed in Representations above.

I first heard this idea from Damien Conway in roughly 2001 at a talk he gave. He said he was considering using it for Perl 6, and I thought it was pretty clever. I don't remember what he called it, and I don't know if he wound up using it, but consider this idea to be his gift to you. Thanks, Damien!

REDACTED


Brendan Eich came up with astoundingly clever performance optimization for the Properties Pattern, which he told me about back in January. I was ready to publish this article, but I told him I'd hold off until he blogged about his optimization. Every once in a while he'd ping me and tell me "any day now."

Brendan, it's October, dammit!

Rolling your own


Needless to say, I've only scratched the surface on performance optimization of the Properties pattern. You can get arbitrarily fancy. The point I'm trying to get across is that you shouldn't despair when you discover your system is unacceptably slow after designing it to use the Properties pattern. If this happens, don't panic and throw out your flexibility – go optimize! The game of optimization can be fun and rewarding in its own right.

Just don't do it before you need it!

Transient properties


While implementing Wyvern, I discovered that making changes to a persistent property list is a wonderful recipe for creating catastrophes.

Let's say some player casts a Resist Magic spell, which boosts her "resist-magic" integer property value by, oh, 30 (thirty percent). Then, while the spell is active, the auto-saver kicks in (writing her enhanced "resist-magic" property value out to the data store along with the rest of her properties), and then the game crashes.

Voilà – the player now has permanent 30% magic resistance!

It doesn't have to be a game crash, either. Any random bug or exception condition (a database hiccup, a network glitch, cosmic rays) can induce permanence in what was intended to be a transient change to the plist. And when you're writing a game designed to be modified at runtime by dozens of programmers simultaneously, you learn quickly to expect random bugs and exception conditions.

The solution I came up with was transient properties. Each object has (logically speaking) two property lists: one for persistent properties and one for transients. The only difference is that transient properties aren't written out when serializing/saving the player (or monster, or what-have-you.)

Wyvern's property-list system has typed values. I haven't talked about Properties Pattern type systems yet, but in a nutshell my property values can be ints, longs, doubles, strings, booleans, archetypes (which is basically any other game object), or "bean" (JavaBean) properties.

My early experimentation yielded the interesting rule that non-numeric transient properties override the persistent value, but numeric properties combine with (add to) the persistent value.

A simple example should suffice. If you have a persistent boolean property "hates-trolls" (and who doesn't, really?), and you accidentally ingest a Potion of Troll Love, then the potion should set a transient value of {"hates-trolls", false} on your character. It overrides the persistent value. There's no combining going on; it just replaces the original.

However, for our "resist-magic" int property, if you put on a ring of 30% magic resistance, it should (by default) add to your current value, which may be a combination of innate resistance and resistances conferred from other magic items and spells.

This numbers-are-additive principle applied pretty uniformly across my entire code base and property corpus, so it's built into the lookup rules for Wyvern's property lists. getIntProperty("foo") must get both the transient and persistent (possibly inherited) values for "foo" and add them before returning the result.

I experimented with different approaches for representing transient properties. Originally I used a kind of hungarian-notation, prefixing transient property names with an @-character ("@foo") and keeping them in the same hashtable as the persistent properties. One advantage of "@" was that it was invalid character in XML attribute names, so it was originally impossible for me to accidentally serialize a transient property.

Eventually I migrated to keeping them in separate (lazily created) tables. This made it easier to deal with interning names (not having to prepend "@" all the time) and generally made bookkeeping easier. I don't remember all the trade-offs involved with the decision anymore (it was about 7 years ago), so you'll have to retread that road yourself if you decide to offer transient properties in your system.

The deletion problem (remix)


Transient properties introduce their own version of deletion problem. You can't just remove the property from the transient list, since the lookup algorithm will just look for it in the persistent list. And you don't want to remove it from the persistent list; that defeats the purpose of using transients.

The solution is similar to what I did for deleting inherited properties: you insert a placeholder into the transient list saying "NOT_PRESENT", and as long as that placeholder is in the list, it's as if the object doesn't have the property.

Note that this implies the existence of two similar API calls: removeTransientProperty for deleting a transient property from the transient list, and transientlyRemoveProperty for temporarily hiding a property from the persistent list.

Persistence


Persisting property lists is a huge topic; I'll just touch on the basics.

For starters, XML and JSON (and for that matter, s-expressions) are all perfectly valid choices for serialization format. You can probably imagine how this works, so I won't beat it to death.

Text-based formats have big wins in readability, maintainability, and bootstrapping (you don't need to create special tools to read and write them).

For performance – both for network overhead and disk storage – you might want to consider designing a compressed binary format. One easy way to test whether this will be a win for you is to take the intermediate approach of gzipping your data to see how well it compresses, and whether it produces a discernable blip in performance.

Wyvern initially used a filesystem trie-like structure for storing its data, but as the number of distinct objects grew to several hundred thousand, I had to switch to a database.

You can use an RDBMS, but you're in for a world of hurt if you try to map the Properties pattern onto a relational schema. It's a tricky problem, and probably isn't one that you want to solve yourself.

I wound up using an RDBMS and just shoving the XML-serialized property list into a text/clob column, and denormalizing the twenty or thirty fields I needed for queries into their own columns. This gets me by, but isn't a happy solution.

What you really want is a hierarchical data store optimized for loose tree structures: in a word, an XML database. At the time I was designing Wyvern's persistence strategy (1998-ish), XML databases were pure vaporware, and even after a few years they were still fairly exploratory and unstable.

Today things are different, and there are many interesting options for XML databases, ranging from 100% free (e.g. Berkeley DBs) through 100% expensive (e.g. Oracle XML).

You might also look into Object databases, but I've never heard of anyone coming through that experience with anything but battle scars to show for it.

Query strategies


Querying goes hand-in-hand with persistence: once you have a bunch of objects in a data store, you'll want to ask questions about them. Producing a High Score List is a good example: you want to compute a function of some set of properties across all the players in your database.

If you're just using the filesystem, you're stuck with grep or its moral equivalent on Windows, which is likely to be painfully slow. So don't do that.

If you're using an RDBMS, and you've serialized your property lists into a single row-per-object clob or text column, then you can use (My)SQL's LIKE and RLIKE operators, or their equivalents, to do free-text searches.

However, your property lists are likely to be hierarchical (e.g. player inventory is a bag, which has its own properties and collection of objects it's holding), and free-text search doesn't understand hierarchy. So this approach is really just a faster version of grep.

Querying is the biggest reason for using an XML database, since it gives you XPath and XQuery as expressive languages that work on XML data about as well (give or take) as SQL works on relational data.

Because you have the advantage of working in "these days" (2008+) as opposed to "those days" (1998), you now have the interesting option of using JavaScript/JSON and JQuery. I don't know much about it, but what little I do know seems promising.

One final approach, which may not scale very well unless you can find a way to parallelize it, is to simply load all the objects into an instance of your server, and use programmatic access to walk the objects and construct your query results manually. Although it requires some infrastructure to make it work (and to make it not crash your system, once you have enough objects), it has the major benefit of giving you a full programming language, which can be useful if you're doing a complex query and your XPath/XQuery skills aren't up to par.

Backfills


Data integrity, a.k.a. Safety, is one of the two biggest trade-offs (the other being performance) you make when you choose to use the Properties pattern. In the absence of a schema, your system is open to property-list corruption through bugs and user error (e.g. typos).

Interestingly, in big companies I've worked at that have strong schema constraints, they still always seem to run into data-integrity problems, so it's not clear how much the schema is really helping here. A schema can certainly help with navigability and performance, but no schema can completely avert data corruption problems.

As soon as you notice you've got bad data, you need to do what many people in the industry term a "backfill": you have to run through all the existing data and fix the problem. Sometimes this is as simple as running a SQL update on a single column. And sometimes it involves writing a complex program that painstakingly computes the inverse of whatever bogus operation created the bad data in the first place.

And sometimes backfills require just winging it, since the lost data may be irrecoverable and you need to use heuristics to minimize the damage. No matter how you store your data and how careful you are about replicating it and backing it up, this kind of thing can happen at pretty much any scale.

The Properties pattern doesn't really introduce anything new to the backfill landscape; all the usual options apply. You'll just need to be mindful that user error (especially mis-typed property names) can make backfills a bit more commonplace, so you should plan to spend a fair amount of time developing a convenient backfill infrastructure for your system.

I should mention, embarrassing as it is, one other option, which I call "lazy backfill", and I've used it extensively. Sometimes I'll notice a data-corruption issue that needs fixing but doesn't really justify a day of my time to fix all at once. So I have a small subsystem in place for player logins and map loads: I iterate through the property lists looking for properties that I've flagged (hardwired in the code) as "bad data", and I call helper backfill functions on the fly to fix just that property list.

This is obviously a hack, and it also imposes some minor performance overhead (probably not detectable via profiling) on logins and map loads, but I'll be honest: it's served me well, and I've fixed at least 20% of my data-corruption problems this way.

Type systems


I've already touched on this a little here and there. Eclipse's AST property lists use an interesting type system that provides a reasonable amount of metadata for each property, although (I think) it stops short of allowing properties to have their own property lists.

JavaScript properties have a small, fixed amount of metadata. Each property has a set of flags. The flags include ReadOnly (can't modify the value), Permanent (can modify the value but can't delete the key), DontEnum (key doesn't show up in iterators but can be read directly), and others depending on the implementation.

Wyvern has its own Java-like flavor of typed properties, largely because I implemented the system in Java long before the advent of auto-boxing, and I needed a convenient way of dealing with primitive types vs. object types. If I were to do it all over again, I probably wouldn't go that route. I would want some sort of scheme for metaproperties (aka "property attributes") — perhaps in a separate per-object metaproperty-list. But I'd simplify the interface and get rid of all the primitive-typed versions of all my has/get/set inherited/persistent/transient property calls.

I won't go into any further detail about type systems, except to say that (a) you can use them to any degree you desire; there's nothing intrinsic to the Properties Pattern that precludes them, and (b) Duck Typing becomes fairly crucial to systems that are designed fully around the Properties Pattern, so if your language has any structural-typing support it'll help.

Toolkits


Wyvern has a Map Editor that allows you to create and edit objects. Since all the game objects are property lists that use the prototype inheritance pattern, the conventional JavaBean approach doesn't work, since the JavaBeans API (which is more or less designed for this problem, except with instance fields) uses Java reflection, and my properties don't have individual getters and setters.

Wyvern wound up with something very similar to a JavaBeans property editor, except it knows how to read, write and display my GameObject property lists.

It wasn't a huge amount of work, but it's something you should keep in mind as you decide whether to use the Properties pattern in your system. If you need a GUI for object edits, you'll probably need to do some custom UI work.

Problems


I've talked about the main problems imposed by the Properties pattern: performance, data integrity, and navigability/queryability. They're all trade-offs; you're sacrificing in these areas in order to achieve big wins in flexibility and open-ended future extensibility for users you may never meet. (You also get huge wins in unit-testability and prototyping speed, but I assume these benefits are obvious enough that I don't need to dwell on them.)

One other problem is reversability: it's hard to back out of the Properties pattern once you commit to it. Once people start adding properties, especially if they're using programmatic construction of key names, you'll have trouble on your hands if you want to try to refactor the whole system to use instance fields and getters/setters. So before you use this pattern, you should put your system through a prototyping phase (ironically enough) to determine whether it will work out as it scales.

Further Reading


I wasn't able to find much, but here are some interesting articles and papers on the subject.

Dealing with Properties [Fowler 1997]

Prototype-based programming (Wikipedia)

Do-it-yourself Reflection [Peter Sommerlad, Marcel Rüedi] (PDF)

Prototype pattern (Wikipedia)

Self programming language (Wikipedia)

Refactoring to Adaptive Object Modeling: Property Pattern [Christopher G. Lasater]

New Updates



Oct 20th 2008: The comments on the article are outstanding. People have pointed out lots of further reading, as well as well-known systems (Atom, RDF) that make extensive use of the pattern at their core. Thanks, folks! This is great stuff.

Oct 20th 2008: Martin Fowler sent me a link to a 1997 paper he wrote on the topic. It's in the Further Reading section. Well worth a read. He mentions a few important considerations that I left out:
  • The (static) dependencies problem — your compiler can't generally help you with finding dependencies on properties, or even tell you what property names are used in your system. He suggests using a registry of permissible property names as one solution. I strongly considered that approach for Wyvern, but wound up relying on a mix of dynamic tracing and static analysis to get me the dependency graph, and it's been "accurate enough" for my needs. In particular, synthesizing property names on the fly happens about as (in)frequently as Reflection happens in Java. So for the most part the dependencies issue is as tractable as it is in Java: "tractable enough".

  • Substituting actions Fowler suggests that it's difficult to replace an existing property access with an action. This is only true in the Java implementation (hence, true for my game). In languages like Python, Ruby and JavaScript 1.5 that support property-access syntax for getters and setters this is a non-issue.
Overall, Martin's take on the pattern is "avoid it when possible", which is sound (if conservative) advice. My take is that everyone's doing it anyway, so we should formalize it. I've used it as the central data model for my 500,000-line multiplayer game for 10 years, and I assert that the benefits vastly outweigh the problems. I also witnessed the pattern's use in Amazon's Customer Service Tools database for some 5 years, and again, the benefits vastly outweighed the downsides.

You just have to know what you're getting into before you dive in, which is sort of the point of my article.

Oct 20th 2008: Fellow Googler Joe Beda mentioned that IE4 originally supported arbitrary attributes on HTML elements, which dramatically extended the flexibility for web developers. Today, no browsers support it, though John Resig claims HTML 5 will fix this. In the meantime, developers use fake css classes and hidden elements; it's a mess. I actually deleted a pretty large rant about this problem from the article. But yeah. It's a problem. When you don't provide the Properties Pattern to people, they find horrible workarounds, which is much worse than anything that can go wrong if you simply support it directly. (Joe mentioned that it posed serious technical problems with the cache, though, so I wouldn't assume it's trivial to add the support back in to browsers today.)

Final thoughts


I haven't covered the whole landscape for this pattern. There are concurrency issues, access-control issues (e.g. in Wyvern, some properties, such as email address, can only be read by very high-level Wizards), documentation issues, and a host of other considerations.

Let me summarize what I think are the key takeaways.

First: this is a critically important pattern. I call it the "Universal" design pattern because it is (by far) the best known solution to the problem of designing open-ended systems, which in turn translates to long-lived systems.

You might not think you're building that kind of system. But if you want your system to grow, and have lots of users, and spread like wildfire, then you are building exactly that kind of system. You just haven't realized it yet.

Second: even though people rarely talk much about this pattern, it's astoundingly widespread. It appears in strongly-typed systems like Eclipse, in programming and data-declarative languages, in end-user applications, in operating systems, and even in strongly typed network protocols, although I didn't talk about that use case today. (Nutshell: a team I know using CORBA got fed up and added an XML parameter to every CORBA API call, defeating the type system but permitting them to upgrade their interface without horking every existing client. Bravo!)

Third: it can perform well! Or at least, "well enough". The playing field for potential optimizations is nearly unbounded, and with enough effort you can reduce just about everything to constant time.

Finally, it's surprisingly versatile. You can use it on a very small scale to augment one teeny component of an existing system, or you can go the whole hog and use it for everything, or just about anything in between. You can start small and grow into it as you become more comfortable with the pattern.

The Properties Pattern is not "just" name/value pairs, although the name/value pair certainly lives at the heart of the pattern.

If you believe Hofstadter, the Properties Pattern (using the Prototype Principle) is an approach to modeling that complements class-based modeling: both are fundamental to the way our brains process symbolic information.

I suspect that if you've read this far, you'll start seeing the Properties Pattern everywhere you look. It's embedded in many other popular patterns and systems, from Dependency Injection to LDAP to DNS. As legacy systems struggle to evolve to be more user configurable and programmable, you'll see more and more of your favorite software systems (and, I hope, languages) incorporating this pattern to varying extents.

Again: I wasn't able to find much literature about this pattern. If you happen to know of books, papers or articles that expound on it in more detail, please link to them in the comments!

I hope you found this interesting and potentially useful. It was definitely more work than my typical posts, so if it doesn't go over well, I'm happy to go back to the comedy routine. We'll see.